


GIFT OF 

PROF. W.B. RISING 




LECT UBE-NOTES 



ON 



THEORETICAL CHEMISTRY. 



BY 



FERDINAND G. WIECHMANN, PH.D., 

\N 

Instructor in Chemical Physics and Chemical Philosophy, School of Mines, 
Columbia College. 



FIRST EDITION. 

FIRST THOUSAND. 



NEW YORK : 

JOHN WILEY & SONS, 

53 EAST TENTH STREET. 

1893. 



COPYRIGHT, 1898, 

BY 
FERDINAND G. WIECHMANN. 



ROBERT DRUMMOND, 

Electrotyper, 

444 & 446 Pearl Street, 

New York. 



SO 

parents, 

11 (SraitttttJr. 



237367 



PEEFACE. 



THE study of theoretical chemistry has not, in general, 
met with that recognition and appreciation which is warranted 
by the interest and importance attaching to this branch of 
chemical science. 

Seeking for an explanation, it appears that to many this 
study presents considerable difficulty, on account of the num- 
ber and variety of themes frequently exhibiting no organic 
connection to which the attention of the student is invited. 

The difficulty is inherent in the nature of the subject, for 
as yet there is no philosophy of chemistry, and work in this 
domain, of necessity resolves itself into a study of the material 
from which such a philosophy may, at some future time, be 
constructed. 

May these pages be of service to those who are entering 
upon a study of these subjects. 

It has been the intention of the writer to offer a general 
view over the wide domain of chemical theory, to exhibit, as 
clearly as might be, the correlation of the many lines of re- 
search along which investigations of the questions of theoret- 
ical chemistry are at present conducted, and, last but not 
least, to point out the practical bearing of its teachings on 

iii 



IV PREFACE. 

problems to be constantly met with in the application of 
chemical knowledge. 

As indicated by its title, this treatise does not pretend to 
offer an exhaustive discussion of the subjects considered; 
volumes have been written on most of the topics to which 
here but a scant chapter or two has been devoted. Indeed, 
it is one of the aims of this book to incite to a thorough 
study of this literature, a literature so constantly increasing 
in scope and in importance. 

With this object in view, a list of works on theoretical 
chemistry is placed at the end of this volume. This list is 
believed to be sufficiently comprehensive to meet the require- 
ments of most students. To facilitate the study of the sub- 
ject from an historical point of view, the titles given are 
arranged in chronological order. 

The periodicals enumerated, barring some few exceptions, 
of course devote but a part of their space to papers of the 
character here considered, yet reference to them has been 
deemed expedient, because frequently important researches 
are first recorded in their columns. 

Considerable prominence has been given in these pages to 
stoichiometry the arithmetic of chemistry and examples 
are freely introduced in illustration of the different principles 
discussed. 

A thorough working familiarity with these principles of 
stoichiometry is essential, and should be acquired by the solv- 
ing of numerous problems ; however, insertion of such prob- 
lems seemed superfluous, in view of the fact that several excel- 
lent collections of this kind have been but recently published. 

In making acknowledgment of his obligations, the writer 
would state that he has considered it his duty, no less than 
his pleasure, to consult all sources of information available. 

No attempt has been made to cite and to give credit for 
individual articles referred to in the journal literature; how- 
ever, the periodicals in which they appear are naimd. 



PREFACE. V 

All books consulted, are marked by asterisks in the bib- 
liography appended, but special mention must be made of 
the writer's indebtedness to the standard works of Kopp, 
Ostwald, and Muir. 

F. G. WlECHMAXX. 

SCHOOL OF MIXES, 
COLUMBIA COLLEGE. 



TABLE OF CONTENTS. 



CHAPTER I. 

INTRODUCTORY. 

PAGE 

Introductory 1 

Origin and Meaning of the Term Chemistry 2 

Aims of Chemistry and of Chemical Philosophy 3 

Definitions 5 

Stoichiometry 5 

CHAPTER II. 

SPECIFIC GRAVITY. 

Definition of Specific Gravity 7 

Standards of Specific Gravity 7 

Relations between Specific Gravity, Mass, and Volume 8 

Determination of the Specific Gravity of Solids 9 

I. By the Balance : 

a. The solid is insoluble in, and heavier than water 9 

b. The solid is insoluble in, and lighter than water 10 

II. By the Specific Gravity Flask : 

a. The solid is insoluble in water 10 

b. The solid is soluble in water 11 

Determination of the Specific Gravity of Liquids : 

I. By the Specific Gravity Flask 11 

II. By Weighing a Solid Insoluble in Water and in the Liquid, 

in Air, Water, and the Liquid 12 

vii 



Vlll CONTENTS. 

PAGE 

III. By the Method of Balanced Liquid Columns 12 

IV. By Areometers 13 

Areometers with Arbitrary Scales , . . . 14 

True value of Baume degrees 14 

Relation between Specific Gravity, Degrees Baume, 

and Degrees Brix 15 

Specific Gravity of Gases and Vapors 17 

Determination of the Specific Gravity of Gases 19 

I. Weighing Equal Volumes of the Standard selected and of 

the Gas the Specific Gravity of which is to be determined. 19 

a. By collecting in a vessel over mercury. (Bunseu.). , . . 19 

b. By displacement 19 

c. By counterbalanced globes. (Regnault.) 19 

II. Effusion Method. (Buuseu.) 19 

Determination of the Specific Gravity of Vapors 20 

I. Weighing a Known Volume of the Vapor taken at an 

Ascertained Temperature and Pressure 20 

Methods of (a) Dumas 20 

(b) Deville 20 

(c) Troost 20 

II. Direct Measurement of the Volume of Vapor produced by 

the Evaporation, in a Closed Space, of a Known Weight 

of the Substance 20 

Methods of (a) Hofmanu 20, 24 

(b) Gay-Lussac 20 

III. The Indirect Measurement of the Volume of Vapor pro- 
duced by the Evaporation, in a Closed Space, of a Known 
Weight of the Substance, accomplished, by measuring the 
Volume of a Liquid or of some Gas, displaced by the 

Vapor 20 

Method of Victor Meyer 20, 26 



CHAPTER III. 

CHEMICAL NOMENCLATURE AND NOTATION. 

Earliest Times 29 

Notation of the Alchemists ... 29 

Nomenclature in the Seventeenth Century. 31 



CONTENTS. IX 



Bergman's System 31 

Black's List of Synonyms 33 

French Systems of Nomenclature 34 

Symbols of Hassenfratz and Adet 37 

Other Systems Proposed 38 

System of the Present 41 

Names and Symbols of the Elements 42 

Names of Compounds 42 

American Spelling and Pronunciation of Chemical Terms 45 

CHAPTER IV. 

ATOMS ATOMIC MASS VALENCE. 

Introductory , 52 

Laws of Chemical Combination 52 

Atomic Mass 53 

Standards of Atomic Muss 54 

Table of Atomic Masses 55 

Determination of Atomic Mass 57 

Direct Determination 57 

Indirect Determination 59 

Aids in Determining Atomic Mass 59 

Vapor Density 59 

Atomic Heat 61 

Isomorphism 63 

Valence 63 

Standard of Valence 64 

Manner of Designating Valence 65 

Variable Valence 65 

Determination of Valence.. . 66 



CHAPTER V. 

CHEMICAL FORMULA. 

Introductory 69 

Determination of Empirical Formulae 69 

Determination of Molecular Formulae 71 



X CONTENTS. 

PAGE 

Determination of Molecular Mass 72 

Method of Chemical Analysis 72 

Method of Vapor-Density Determination 72 

Methods based on Properties of Substances when in Solution. . 73 

Method A. Osmotic Pressure 73 

Method B. Lowering of the Vapor-pressure 74 

Method C. Elevation of the Boiling-point 75 

Method D. Depression of the Freezing-point 75 



CHAPTER VI. 

THE STRUCTURE OF MOLECULES. 

Introductory 78 

Molecular Volume 79 

Molecular Refraction 81 

Magnetic Rotation of the Plane of Polarized Light 84 

Isomerism 84 

Stereochemistry 85 



CHAPTER VII. 

CHEMICAL EQUATIONS AND CALCULATIONS. 

Definitions 89 

Oxidizing Agents 91 

Reducing Agents 92 

Laws of Chemical Interchange 92 

The Writing of Chemical Equations 93 

The Analytical Method 93 

The Method of Negative Bonds 96 

The Algebraic Method 97 

Calculations of Chemical Problems 99 

Calculation of the Molecular Mass of a Substance 99 

Calculation of the Amount of any Constituent in a Compound. 100 
Calculation of the Amount of a Compound which can be pro- 
duced from a given Amount of any of its Constituents 100 

Calculation of the Percentage Composition of a Compound 

from its Formula. . . 101 



CONTENTS. XI 

PAGE 

Calculation of the Chemical Formula of a Compound from its 
Percentage Composition 101 

a. Calculation of the empirical formula 101 

b. Calculation of the molecular formula 101 

c. Calculation of the formulae of minerals 101 

Methods of Indirect Analysis 107 

I. The Residue Method 107 

II. The Substitution Method 108 

III. The*Method based on Numerical Differences between Mo- 
lecular Masses. 108 

a. The components of the mixture have one constituent in 

common 108 

b. The components of the mixture have more than one con- 

stituent in common. . Ill 



CHAPTER VIII. 

VOLUME AND WEIGHT RELATIONS OP GASES. 

Volume Relations of Gases 115 

Law of Volumes 119 

Relations between Mass and Volume in Gases 124 

Analysis of Gases 128 

Introductory 128 

Proximate Analysis 128 

Method of Explosions 130 



CHAPTER IX. 

THE PERIODIC LAW. 

Introductory 133 

The Periodic Law 134 

Newlands' Table 134 

Mendeleeff's Table 136 

Lothar Meyer's Table 137 

Atomic Analogues 139 

Mendeleeff's Predictions 139 

Importance of the Periodic Law 139 



CONTENTS. 



Graphic Curves 139 

Periodicity of the Properties of Elements and Compounds 141 



CHAPTER X. 



SOLUTIONS. 

* 

Definition 143 

Solutions of : 

Gases in Gases 143 

Gases in Liquids 144 

Gases in Solids. 145 

Liquids in Gases 145 

Liquids in Liquids 145 

Liquids in Solids 147 

Solids in Gases 147 

Solids in Liquids 147 

Solids in Solids 149 

Dilute Solutions 149 

Osmotic Pressure 150 

Measurement of Osmotic Pressure , 151 

Diffusion... . 153 



CHAPTER XI. 

ENERGY CHEMICAL AFFINITY. 

Introductory 155 

Measurement of Force 155 

The Gravity Unit of Force 156 

The Absolute Unit of Force 156 

Relation between Gravity Units and Absolute Units 156 

Measurement of Energy 157 

The Gravity Unit of Work 157 

The Absolute Unit of Work 157 

The Law of the Conservation of Energy 157 

Chemical Affinity 158 

Hypotheses regarding the Nature of Chemical Affinity 159 



CONTENTS. Xlll 

PAGE 

Measurement of Chemical Affinity 161 

Laplace 161 

Morveau , Gay-Lussac, etc 161 

Weuzel 161 

Lavoisier 161 

Tables of Affinity 162 

Geoffrey 162 

Bergman 163 

Kirwan 163 

Berthollet 163 

Guldberg and Waage 164 

Clausius and Maxwell 164 

Electrical Methods. . . 165 



CHAPTER XII. 



THERMAL RELATIONS THERMO CHEMISTRY. 

Introductory 167 

Temperature 167 

Heat Units 168 

Mechanical Equivalent of Heat 168 

Latent Heat 169 

Specific Heat 169 

Determination of Specific Heat 169 

I. The Method of the Ice Calorimeter 170 

II. The Method of Mixtures 171 

III. The Time Method 172 

Combustion 173 

Calorific Power 173 

Calorific Intensity 174 

Thermo-chemistry 178 

Methods employed in Thermo-chemistry 178 

Laws of Thermo-chemistry 179 

Exothermous and Endothermous Compounds 181 

The Language of Thermo-chemistry 181 

Energy-equations ,,.,,,.,.,.,.,,., 183 



XIV CONTENTS. 

CHAPTER XIII. 

PHOTO-CHEMISTRY. 

PAGE 

Introductory 187 

Chemical Union 187 

Chemical Decomposition 187 

Physical Changes 189 

Mode of Action 190 

Measurement of the Chemical Activity of Light 191 

CHAPTER XIV. 

ELECTRO-CHEMISTRY. 

Introductory 192 

Electrolysis 193 

The Ion Theory 193 

Electrolytic Dissociation 194 

Electrical Units 196 

Quantitative Relations 199 

BIBLIOGRAPHY. 

Periodicals 203 

Books . 204 



LECTURE-NOTES 

ON 

THEORETICAL CHEMISTRY. 



CHAPTER I. 
INTRODUCTORY. 

KNOWLEDGE consists in an intelligent perception and 
understanding of facts and ideas. 

Science is systematized knowledge. 

A science which has been established solely by the process 
of reasoning, which deduces theories from ideas, which does 
not base on experience, is termed a deductive science; the 
pure mathematics will serve as an illustration of this type. 

A science which rests on observation and experience, which 
owes its existence to the inference of theories and the evolu- 
tion of laws from observed facts, is an inductive science; 
chemistry is a representative science of this character. 

The aims pursued by the devotees of chemistry have at 
various times been so very different, that chemistry, in the 
sense in which the term is now understood, is a science of 
comparatively recent origin. 

The very beginning of chemical history can be traced back 
to the remote past. However, until the fourth century no 
attempt was made to collate the chemical facts then known, 
or to employ them for the attainment of any definite purpose. 

1 



2 LECTURE-NOTES OK 'THEORETICAL CHEMISTRY. 

The era beginning with the fourth century and extending 
to the first quarter of the sixteenth century may be denoted 
as the age of alchemy. From that time on, and to the middle 
of the seventeenth century, chemistry was made to serve the 
interests of medicine, and this period is designated as the age 
of medical chemistry or iatro-chemistry. It was with the ter- 
mination of this era that chemistry entered upon the pursuit 
of independent and well-defined aims. 

Origin and Meaning of the Term Chemistry. The origin 
of the word chemistry is involved in some doubt. The first 
one to record this expression was, it seems, Julius Maternus 
Firmicus, who lived about 340 A.D. 

This author wrote a treatise on astronomy entitled " Mathe- 
sis." Among other matters there is in this work a reference 
to the influence exercised on the inclinations of mortal man 
by the relative position which the moon and a planet may 
chance to hold at the hour of his birth. In this instance 
the word " Alchemise," or, as some manuscripts have it, 
" Chemiae," is used for the first time in a sense similar to that 
in which the expression chemical knowledge is used at the 
present time. This author, however, gives no explanation or 
definition of the term, apparently assuming the word " Chemia" 
to be well known. 

The true meaning of the word chemistry has also been a 
matter of considerable doubt. Two appellations, " Chemia" 
and "Chymia," have been in use for a long time, and these 
terms admit of diiferent interpretations as to their origin. 
Of these two expressions the term " Chemia" is the older, 
" Chymia" being of a more recent date. 

It is most probable that the first attempt to collate chemical 
facts and to apply them to the solving of any one task, was 
made in Egypt. It is also likely that the art which was the 
result of this attempt, was named from the country where it 
originated. 

According to Plutarch, about 100 A.D., the original name 



INTRODUCTORY. 3 

of Egypt was Xrjuia, Chemia. This name was given to it on 
account of the black color of its soil. The black of the eye, 
the pupil, as the symbol of the dark and mysterious, was also 
denoted by the same term. It seems, therefore, most proba- 
ble that the word chemistry originally meant Egyptian knowl- 
edge, and later on, it was frequently termed the secret, or the 
black art. 

Zosimus, about 400 A.D., used the term XWi** to indicate the 
whole of the secret art which was said to have been imparted 
to man by superior beings, and in which the art of making 
gold and silver was included. 

In later times the expression " Chymia" was assigned to all 
knowledge of this description, and the use of this term has 
led to an attempt to account in a different way for the name 
of this science. It is said to have been derived from the 
Greek word ^ujwo's", a fluid or sap, and it was inferred that 
thereby the art to work with solutions was indicated. This 
word has the same root as the Greek word ^eo?, to pour out, 
to make fluid, to melt; yet for various reasons the above infer- 
ence concerning the origin of the word chemistry, seems un- 
tenable. 

Aims of Chemistry and of Chemical Philosophy. The aim 
of chemistry is the study of matter the constitution of 
matter, its properties and its transformations. This indicates 
at once the wide range and scope of this branch of knowledge. 

In order to facilitate the work and to permit of a compre- 
hensive view over the whole field, a division of the subject into 
various sections has been made, as, for instance, into general 
chemistry, applied chemistry, analytical chemistry. But 
whatever the classification into groups or sections, the task 
of chemical philosophy is to generalize all information gained 
in the study and in the laboratory, to seek out the relation 
between chemical phenomena and their causes, to trace the 
laws which govern these phenomena, and ultimately, by the 
comparison and co-ordination of numerous data secured by 



4 LECTtJRE-KOTES OK THEORETICAL CHEMISTRY. 

observation and experiment, to deduce and establish the 
fundamental principles of chemical science. 

Chemistry, as a philosophical system, is as yet in the period 
of evolution, and probably is still far from the form in which 
it will ultimately rest. 

Newly-discovered facts call for explanation ; new hypotheses 
are constantly appearing; new theories displace the old. As, 
however, in the development of all sciences, so in chemistry, 
no advance can ever displace a truth once discovered and 
established, although the form in which it is expressed, may 
have to be greatly modified or extended. 

It is important to assign their proper value to inferences 
and conclusions which may be drawn from observations, and 
care should be taken to employ correctly the terms hypothesis, 
theory, and law. 

An hypothesis is a supposition provisionally adopted to 
account for and to explain certain facts; it is a tentative con- 
jecture concerning the nature and cause of phenomena. 

A theory represents the logical deductions ' that can be 
drawn from a working hypothesis; it is an exposition of 
general principles, and is intended to exhibit the relations 
existing between the parts of a systematic whole. 

The crucial test as to the value and validity of any hypoth- 
esis or theory rests of course in its concordance with the facts 
ascertained by experiment and observation. 

The discovery and establishment of any fact or facts which 
may not be in harmony with a given hypothesis or theory, 
of course forces the abandonment, or at least the modifi- 
cation, of the latter, and calls for the formulation of some 
theory which shall take due account of such newly-ascertained 
facts. 

A law may be defined as a mode or order of sequence. A 
law must not only embrace all known facts and phenomena 
to which it refers, but it must also be able to account for all. 
phenomena of like character which may ever be discovered 



INTRODUCTORY. 5 

In fact, a law must, to a certain extent, be capable of predict- 
ing the existence of such phenomena. 

Definitions. There are a few terms used in chemical science 
which are also frequently employed in general language. As 
a clear conception of the precise meaning assigned in science 
to these terms is essential, the following definitions may not 
be superfluous: 

Matter. That which has extension, which occupies space; 
which is perceptible by the senses; which constitutes the 
universe. 

Mass. Any portion of matter appreciable by the senses. 
Also, the amount (quantity) of matter in a substance. 

Molecule. The smallest particle into which matter can be 
divided without destroying its identity. 

Atom. The smallest quantity of matter that can enter into 
chemical combination. 

Weight. The amount of attraction between two masses; 
in a restricted sense, the amount of attraction of the earth on 
a substance. ' 

Volume. The amount of space occupied by a substance. 

Motion. Change of position. 

Rest. Permanence of position. 

Work. The overcoming of resistance. 

Energy. The power of doing work; the cause of all 
change experienced by matter. 

Force. Included in above definition of energy; in a more 
restricted sense, any cause which tends to produce, change, or 
destroy motion. 

Stoichiometry. The term stoichiometry is derived from the 
Greek o-roz^ezov, elementary substance, and /^erpov, measure. 
It treats of the quantitative relations of chemical substances. 

The idea that salts contain acid and alkali in definite pro- 
portions, seems to have been held at a very early date; at 
least, certain passages in the writings of Geber, an alchemist 
of the eighth century, are quoted in support of this view. 



6 LECTURE-NOTES ON" THEORETICAL CHEMISTRY. 

Definite evidence of it is certainly found in the writings of 
Van Helmont, 1640, and in 1699 Homberg made an investi- 
gation in order to ascertain the quantities of different acids 
which would combine with a stated amount of alkali. 

The outlines of stoichiometrical teachings, to the extent 
to which they had been developed up to that time, were pub- 
lished by a German, Carl Friedrich Wenzel, in 1777.* 

The term stoichiometry was introduced by another Ger- 
man chemist, Jeremias Benjamin Richter, most of whose 
writings treat of the application of mathematics to chemistry. 
In 1792-94 this author published a work of three volumes 
relating to stoichiometry. \ 

The growth of this branch of chemistry was by no means 
rapid. The law of combination in definite proportions was 
first enunciated by Proust in 1801, with reference to oxides. 
The law of multiple proportions was discovered by Dalton. 
Dalton's views, which he had conceived as early as 1804, were 
published only in 1807 in Thomson's "System of Chemistry." 
In the year following, Dalton issued his own work, " New 
System of Chemical Philosophy/' in which his views and 
teachings were fully stated. 

Active among the workers who advanced theoretical chem- 
istry in the latter part of the eighteenth, and in the earlier 
part of this century, were Lavoisier, Gay-Lussac, Von Hum- 
boldt, Berzelius, and Avogadro. 

At the present time, chemistry is rapidly approaching the 
condition of an exact science, and in consequence, the study 
of stoichiometry is one of growing importance; even now it 
would seem, that the day is not far distant when chemistry 
shall become firmly established on a mathematical basis. 

* Vorlesungeii iiber die chemische Verwandtscbaft der Kftrper. 
f Stochiometrie oder Messkunst chymischer Elemente. 



SPECIFIC GRAVITY. 



CHAPTER II. 
SPECIFIC GRAVITY. 

Definition of Specific Gravity. The specific gravity of a 
substance is the ratio of its mass to the mass of an equal 
volume of some other substance taken as unity. 

Standards of Specific Gravity. The choice of standards of 
specific gravity has been an arbitrary one. . For solid and for 
liquid substances the standard now universally adopted, is 
pure water at its greatest density, that is, at 4 C. 

The standard selected for gases and vapors is either hy- 
drogen, air, or oxygen, perfectly dry and at a temperature of 
C. and under a pressure of 760 mm. of mercury; these con- 
ditions of temperature and pressure are termed the standard 
conditions. 

The specific gravity of any substance, A, is found by divid- 
ing the mass of one volume of A by the mass of one volume 
of the substance selected as the standard. 

Let W = mass of one volume of A ; 

W mass of one volume of standard. 

Then Sp. Gr. of A = ^. 

Specific gravity, or, as it is frequently termed, relative mass, 
is entirely independent of the system of weights in which the 
masses of substance and standard are expressed. 

Special attention should be paid to the distinction between 
the terms mass and weight. Mass, is the amount of matter in 
a substance, and is an invariable quantity ; weight, expresses the 



8 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

force with which the substance is attracted by the earth, and 
varies according to the place where it is measured. 

Relations between Specific Gravity, Mass, and Volume. 

In the metric system the relation between the unit of mass 
and that of volume is an intimate one. One cubic centimetre 
of pure water at 4 C. has a mass of one gramme. Therefore, 
in all specific-gravity determinations of solids and liquids, 
where the values are expressed in the metric system, W of 
the preceding formula may be replaced by V, signifying the 
volume of the water displaced. 

Let W.= mass of one volume of A', 

V = mass of one volume of standard. 

Then the formula becomes : 

Sp. Gr. = -^. 

From this are deduced the values of W and of V\ 
W= V-x Sp. Gr.; 



Sp. Gr: 

In the formula, 

W- Vx Sp. Gr. 

Sp. Gr. stands for the specific gravity referred to water. If 
the Sp. Gr. is referred to hydrogen, as in the case of gases, 
this value must be reduced to the water standard before using 
it in the formula. 

The Sp. Gr. of hydrogen referred to water is 0.0000896; 
the reduction is therefore easily effected by simply multiply- 
ing by this value. The formula then reads : 

W= VX Sp. Gr. X 0.0000896. 



SPEC I F I C G K A V IT Y . 

The weight of one cubic decimetre or litre of hydrogen gas 
at the standard temperature and pressure is 0.089578 gramme, 
or, for all practical purposes, 0.0896 gramme. 

In order to simplify calculation, Prof, von Hofmann pro- 
posed that this value be introduced into chemistry as a unit 
of weight. It is termed the crith. The crith is therefore 
denned, as the weight of one cubic decimetre (litre) of hydro- 
gen gas at the standard temperature and pressure, and is 
equal to 0.0896 gramme. 

Let We =. the weight of a gas in criths; 
Wg = the weight of a gas in grammes; 
V the volume of this gas in litres. 
Then We = V x Sp. Gr. 
and Wg = We X 0.0896. 

To ascertain the specific gravity of solids, liquids, and gases, 
numerous methods have been devised to meet the various 
conditions under which the determinations may be presented; 
but the principle underlying these devious methods, is of 
course always the same. The following examples will illus- 
trate some of the more commonly occurring problems. 

Determination of the Specific Gravity of Solids. 

I. By the Balance. This method is based on the principle 
of Archimedes : a body immersed in a liquid loses in weight, 
an amount equal to the weight of the liquid displaced. 

a. The solid is insoluble in, and heavier than, water. 
EXAMPLE : 

Weight of solid in air = 10.000 

" " "water = 8.000 

Weight of water displaced by the solid is: 
10.000 
8.000 

2.000 
Sp. Gr, = = 5.0. 



10 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

1. The solid is insoluble in, and lighter than, water. 

As the solid is lighter than water, there must be attached to 
it a piece of some other substance which is heavy enough to 
immerse the combination. The substance thus attached is 
called a sinker. 

EXAMPLE : 

Weight of solid in air =25.350 

" sinker in air = 11.000 

" " solid and sinker in water = 5.100 

Specific gravity of sinker 9.000 

Weight of solid in air = 25.350 

" " sinker in air.. .. = 11.000 



" solid + sinker in air = 36.350 

Specific gravity of sinker = 9.000 

Weight of sinker in air = 11.000 

Volume of sinker = y = 1.222 

This expresses also the loss in weight the sinker would sustain if 
immersed alone in water. 

Weight of solid -f sinker in air =36.350 

" " " " "water = 5.100 

Loss of weight of solid + sinker in water = 31.250 

" " " " sinker in water = 1.222 



" " " " solid in water = 30.028 

/^O. oOU r\ 

S P- GI> - = 30.028 = ' 844 - 
II. By the Specific-gravity Flask (Pyknometer). 

a. The solid is insoluble in water, 

This method is especially indicated in cases where the 
solid is in a fine state of division ; for instance, in the case of 
a powder. 

EXAMPLE : 

Weight of solid in air = 10.000 

" " pyknometer =. 5.035 

" " " + water =40.535 

" " " -f solid and water* =46.755 

* This fills the space in the fl^sk not occupied by the solid. 



SPECIFIC GRAVITY. 11 

Weight of pyknometer + water =40.535 

" " " = 5.035 

" " water... .. =35.500 



Weight of pyknometer -{- solid -f- water = 46.755 

" " ..= 5.035 



" solid + water 41.720 

" solid . . . = 10.000 



" " water in space not occupied by the solid = 31.730 
The solid therefore occupies a space of 35.50 less 31.72 = 3.78 c. 



b. The solid is soluble in water. ' 

Some liquid must be used in which the solid is not soluble; 
alcohol, naphtha, turpentine, or oil are usually employed. 
The specific gravity of the liquid used, with reference to 
water, and the specific gravity of the solid with reference to 
the liquid used, must be ascertained. A multiplication of 
these two values represents the specific gravity of the solid 
with reference to water. 

EXAMPLE : 

Weight of solid in air .......................... = 400.CO 

" " "turpentine ................... =182.50 

" "an equal volume of turpentine ....... = 217.50 

400 
Sp. Gr. of solid referred to turpentine = J~ . . . = 1.84 

Sp. Gr. of turpentine referred to water .......... = 0.87 

Sp. Gr. of solid referred to water = 1.84 X 0.87.. = 1.60 

Determination of the Specific Gravity of Liquids. 

I. By the Specific-gravity Flask (Pyknometer). 

EXAMPLE : 

Weight of pyknometer .......... .............. = 5.000 

-|- water .................. =20.000 

+ liquid .................. = 17.000 



LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

"Weight of pyknometer -f water =20.000 

" . . = 5.000 



water = 15.000 



Weight of pyknometer -f liquid = 17.000 

" " = 5.000 

"liquid = 12.000 

Sp. Gr. of liquid = ^? = 0.80 

10. 00 

II. By Weighing a Solid Insoluble in Water and in the 

Liquid, in : Air, Water, and the Liquid. 
EXAMPLE : 

Weight of solid in air = 12.000 

" " ''water - 7.000 

" " "liquid = 8.000 

Weight of solid in air = 12.000 

" " "water = 7.000 

" " water displaced = 5.000 



Weight of solid in air = 12.000 

" " "liquid = 8.000 

" liquid displaced = 4.000 

Sp. Gr. of liquid = j^. . . = 0.80 

o.U 

III. By the Method of Balanced Liquid Columns. This 
method depends on the principle of the equilibrium of 
liquids in connected vessels. Two vertical glass tubes are 
connected at their upper ends with each other, and with the 
chamber of an air-syringe. The lower end of one of these 
tubes dips into water; that of the other tube dips into the 
liquid, the specific gravity of which is to be ascertained. The 
air is partially exhausted from the upper part of the two tubes, 
and in consequence, the water and the liquid rise. Closing 
the stop-cock which connects the tubes with the air-syringe, 
the liquids will remain standing at a certain height in their 
respective tubes, the two columns being in equilibrium. The 



SPECIFIC GRAVITY. 13 

specific gravity of the liquid is found, by dividing the height 
of the column of water by the height of the column of liquid. 

EXAMPLE : 

Height of column of water =80 cm. 

" " " "liquid =60 cm. 

QA 

Sp. Gr. of liquid = ^ = 1.333 

IV. By Areometers. This is an indirect method of ascer- 
taining the specific gravity of fluids. The instruments em- 
ployed for the purpose are made of glass or of metal. They 
consist of a bulb or float filled with air, a stem placed above 
this float and bearing a scale, and a smaller bulb, the counter- 
poise, placed beneath the float and weighted with mercury or 
shot, so as to keep the instrument in an upright position when 
placed in a fluid. 

A body immersed in a liquid floats, when it has displaced 
an amount of the liquid equal in weight to its own weight. 
It is therefore evident, that an areometer will sink more 
deeply in a liquid of less density, than it will in a liquid of 
greater density. 

Areometers are provided with scales which either indicate 
specific-gravity values, or else bear an arbitrary graduation. 

In instruments graduated to show specific-gravity values, 
the spaces between successive degrees are unequal. 

These areometers are constructed on the principle, that 
equal differences of specific gravities are indicated by quan- 
tities proportional to the differences of the reciprocals of the 
specific gravities. 

On areometers graduated according to an arbitrary scale, 
the divisions are usually equal. Different kinds of areo- 
meters with arbitrary scales are employed in the arts and in- 
dustries. 

To determine the specific gravity of a liquid by means of 
an areometer, due attention being paid to the temperature of 
the liquid, the instrument is placed in the liquid, and that 



14 LECTURE-NOTES ON" THEORETICAL CHEMISTRY. 

degree of the scale which is in contact with the surface of the 
liquid, is noted. 

If the areometer is graduated according to specific-gravity 
values, the figure thus indicated denotes the specific gravity 
of the liquid. If the graduation on the instrument is accord- 
ing to some arbitrary scale, conversion into the corresponding 
specific-gravity value must be made by calculation, or else is 
determined by aid of tables prepared for the purpose. 

AREOMETERS WITH ARBITRARY SCALES. Among the 
numerous areometers provided with arbitrary scales, those 
devised by Antoine Baume in 1768, and bearing his name, 
are probably used more extensively than any other kind. 

Although Baume described very accurately the manner in 
which he obtained the scales for his two instruments the 
one for liquids heavier, the other for liquids lighter, than 
water yet, in the course of time, the makers of these in- 
struments deviated from his directions, and in consequence 
there resulted great confusion as to the actual relation 
between the values of the so-called Baume degrees and 
specific gravity. 

True Value of Baume Degrees. In a paper delivered by 
C. F. Chandler before the National Academy of Sciences in 
1881, there are given no less than twenty-three different 
scales for liquids heavier than water and eleven different 
scales for liquids lighter than water, no two of which are 
identical, and not one of which was made in exact accordance 
with the original directions of Baume. ID order to ascertain 
the true value of these degrees in terms of specific gravity, 
the original French directions were secured, Baume's experi- 
ments were most carefully repeated, and the following table, 
by C. F. Chandler and the author, gives, as the result of these 
investigations, the true values of Baume's degrees for liquids 
heavier than water, calculated by the formulae : 

_ PXjl. p _ n 

n ~P-l' ~- n-d' 



SPECIFIC GRAVITY. 



15 



In which P = the specific gravity ; d = the Baume de- 
gree; n - the modulus.* = 1. and 15 = 1.1118988, by 
the modulus 149.04969. 

[Temperature 10 R. = 12.5 C. = 54.5 R] 



Baum6 
Degrees. 


Specific 
Gravity. 


Baume 
Degrees. 


Specific 
Gravity. 


Baum6 
Degrees. 


Specific 
Gravity. 





1.00000 


26 


1.21129 


52 


1.53580 


1 


1.00675 


27 


1.22122 


53 


1.55179 


2 


1.01360 


28 


1.23131 


54 


.56812 


3 


1.02054 


29 


1.24156 


55 


.58479 


4 


1.02757 


30 


25199 


56 


.60182 


5 


1.03471 


31 


.26260 


57 


.61923 


6 


1.04194 


32 


.27338 


58 


.63701 


7 


1.04927 


33 


.28436 i 


59 


1.65519 


8 


1.05671 


34 


.29552 


60 


1.67378 


9 


1.06426 


35 


.30688 


61 


1.69279 


10 


1.07191 


36 


.31844 


62 


.71223 


11 


1.07968 


37 


1.33021 


63 


.73213 


12 


1.08755 


38 


1.34218 


64 


.75250 


13 


1.09555 


39 


1.35438 


65 


.77335 


14 


1 . 10366 


40 


1 36680 


66 


.79470 


15 


1.11189 


41 


1.37945 


67 


.81657 


16 


1.12025 


42 


1.39234 


68 


.83899 


17 


1 . 12873 


43 


1.40547 


69 


1.86196 


18 


1.13735 


44 


1.41885 


70 


1.88551 


19 


1.14609 


45 


1.43248 


71 


1.90967 


20 


1 . 15497 


46 


1.44638 


72 


1.93446 


21 


1.16399 


47 


1.46056 


73 


1.95989 


22 


1.17316 


48 


1.47501 


74 


1.98601 


23 


1.18246 


49 


1.48975 


75 


2.01283 


24 


1.19192 


50 


1 . 50479 


76 


2.04038 


25 


1.20153 


51 


1.52014 







Relation between Specific Gravity, Degrees Baume, and 
Degrees Brix. An areometer which is most extensively used 
in the sugar industry to gauge the density of saccharine solu- 
tions, is known as the saccharometer of Balling or Brix. 



* That part of an areometer which is immersed when the instrument 
floats in water. 



16 LECTURE-XOTES OX THEORETICAL CHEMISTRY. 

This instrument bears a scale of 100 degrees, and its read- 
ings indicate the percentage of sucrose in aqueous solutions. 

Comparison between specific-gravity values, degrees Baume, 
and degrees Brix, can be made by means of the following for- 
mulae, due to von Lorenz.* The temperature at which these 
relations obtain, is 17.5 C. 

SPECIFIC GRAVITY AXD DEGREES BRIX. 

Let d = specific gravity, 
s degrees Brix. 

For the range of : 
35 Brix., ..< 



29375 100s 
35 70 Brix., ..d = 



70 100 Brix.. ..d = 



35163 - 100s 
42067 + 92s 



42908 - 100s 
DEGREES BRIX AXD SPECIFIC GRAVITY. 

For the range of: 



49908^ 42067 
1.350881.55785.. . .s = 



WOd -f- 92 

SPECIFIC GRAVITY AXD DEGREES BAUME. 

Let d = specific gravity, 
n = degrees Baume. 

146.78 



d = 



146.78 - n 



* Oesterreichisch-Ungariscbe Zeitschrift fiir Zuckeriudustrie uud 
Landwirthscbaft, 1891, Vol. XX. p. 571. 



SPECIFIC GRAVITY. 17 

DEGREES BAUME AXD SPECIFIC GRAVITY. 

n = 146.78^-^* 

DEGREES BRIX AXD DEGREES BAUME. 

Let s = degrees Brix, 

n = degrees Baume. 
For the range of: 

10 -4- 20P7 
0.00 19.60 Baume s = 



19.60 38.12 Baume 
38.12 52.56 Baume 



1195 n 
433 -f 814.5ft, 

488 - n 
1342 -f 457.2/i 



306.3 - n 

DEGREES BAUME AND DEGREES BRIX. 

For the range of : 
35 Brix., ..w = 



An extensive table, exhibiting the corresponding values of 
specific gravity, degrees Brix, and degrees Baume for pure 
sugar solutions from to 100 per cent, at 17.5 C., has been 
calculated by Mategczek and Scheibler,* and the data of this 
table agree very closely with the results obtained by calcula- 
tion with the formulae of von Lorenz. 

Specific Gravity of Gases and Vapors. 

In making determinations of the specific gravity of gases 
and vapors, great attention must be paid to the conditions 
of temperature and pressure obtaining at the time, for, 

* Loc. cit. ; also, Wiechmami, Sugar Analysis. 



18 LECTURE-tfOTES ON THEORETICAL CHEMISTRY. 

according to the Law of Charles, the volume of a gas varies 
directly as the temperature, and, according to the Law of 
Mariotte,* the volume of a gas varies inversely as the pressure. 

The standard of specific gravity of gases and vapors gen- 
erally adopted is pure, dry hydrogen, or pure, dry air, at 
the temperature of C. and under the pressure of 760 mm. 
of mercury. 

Specific-gravity values determined in terms of one of 
these standards, can readily be expressed in terms of the 
other. 

One litre of hydrogen under the standard conditions 
weighs 0.0896 gramme. One litre of air under the standard 
conditions weighs 1.293 grammes. 

The specific gravity of hydrogen referred to air as standard 
is, therefore, 



and the specific gravity of air referred to hydrogen as stand 
ard, is equal to, 

1 9QQ 

- = 14.43. 



0.0896 

Hence, if the specific gravity of a gas or vapor be given in 
terms of hydrogen as standard, this value multiplied by 
0.0693 will express its specific gravity with reference to air 
as standard. 

If the specific gravity is referred to air as standard, the 
value given multiplied by 14.43 will express the specific 
gravity on the hydrogen basis. 

The principal methods employed in the determination of 
the specific gravity of gases and vapors are the following. 

* Also known as the Law of Boyle. 



SPECIFIC GRAVITY. 19 

Determination of the Specific Gravity of Gases. 

I. Weighing Equal Volumes of the Standard selected and 
of the Gas the Specific Gravity of which is to be determined. 

a. By collecting in a vessel over mercury. (Bunsen.) 

b. By displacement. 

The gas the specific gravity of which is sought, is passed 
into a vessel of known volume, and displaces an inert gas 
which this vessel contains. The temperature is kept con- 
stant throughout the experiment. 

c. By counterbalanced globes. (Regnault.) 
These methods require the following data : 

P = the weight of the empty vessel, in air. 

P' = the weight of the vessel filled with the gas, in air. 

V = the capacity of the vessel in cubic centimetres. 

v = the volume of the residual air in cubic centimetres. 

H = height of barometer ) 

[ at which P' is found. 
t = the temperature ) 

H 9 = height of barometer \ 

m I at the time of sealing or closing 

T = the temperature of V , , 

, , , f the vessel. 

the bath ) 

k = the coefficient of cubical expansion of the material of 

the vessel. 
0.00367 the coefficient of expansion of a gas at constant 

pressure. 

The specific gravity referred to hydrogen, is calculated by 
the formula: 

0.0012933. (F-tQ.jy 

s r (1 + 0.00367 T). 760 

~F 1+0.00367. yi H' X 0.00008958 

V 1+0.00367. J760. (1+0.00367 T)' 

II. Effusion Method. (Bunsen.) This method is based on 
the principle that the specific gravity of gases varies directly 
as the square of the time of effusion of equal volumes.* 

* Sometimes expressed in this form : The rates of effusion are in- 
versely as the square roots of the specific gravities of the gases. 



20 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

Equal volumes of the standard gas, and of the gas the 
specific gravity of which is to be determined, are allowed 
to escape through a very small aperture from the vessel in 
which they are contained, and the time required by each to 
do this, is noted. 
EXAMPLE : 

One volume of air effuses ID 180 seconds. 

One volume of gas the specific gravity of which is sought, effuses in 
120 seconds. 

ISO' 2 : ISO 2 ::l: xi 
32400 : 14400 : : 1 : a?; 

* = 0.44. 
Hence, 8p. Gr. of the gas referred to air is 0.44. 

Determination of the Specific Gravity of Vapors. 

The specific gravity of a vapor is usually determined by: 

I. The Weighing of a Known Volume of the Vapor taken 
at an Ascertained Temperature and Pressure. 

Methods of (a) Dumas, 
(5) Deville, 
(c) Troost. 

II. The Direct Measurement of the Volume of Vapor pro- 
duced by the Evaporation in a Closed Space of a Known 
Weight of the Substance. 

Methods of (a) Hofmann, 
(b) Gay-Lussac. 

III. The Indirect Measurement of the Volume of Vapor 
produced by the Evaporation in a Closed Space of a Known 
Weight of the Substance, accomplished by measuring the 
Volume of a Liquid or of some Gas displaced by the Vapor. 

Method of Victor Meyer. 

I. Dumas' Method. To calculate the specific gravity of a 
vapor by Dumas' method, it is necessary to ascertain the 
weight of a known volume of this vapor at a known temper- 
ature and under a known pressure, and to divide this value 



SPECIFIC GRAVITY. 21 

by the weight of the same volume of air, or hydrogen, at 
the same temperature and under the same pressure. 

A glass vessel filled with dry air or hydrogen is weighed. 
Then the substance, the specific gravity of whose vapor is to 
be determined, is introduced and vaporized. When the ves- 
sel is filled completely and exclusively with this vapor, the 
neck of the vessel is sealed and the vessel is reweighed. 

The formula by which the density of a vapor determined 
by Dumas' method, and referred to air as unity, is calcu- 
lated, is the following: 

o -, # + c a 

Specific gravity = - . 

In which: 

a = the weight of the vessel; 

b = the apparent weight of the vessel and the vapor; 
c = the weight of the air displaced by the vessel; 
W= the weight of an equal volume of air at the same 
pressure and temperature. The increased volume 
of the vessel at the higher temperature must of 
course be taken into account. 

Before illustrating the application of this formula by an 
example, the manner of calculating some of the values used 
in this formula should be explained. 

Suppose it were required to ascertain the weight ( TF) of 
dry air at a temperature t and at a pressure H, contained in a 
glass vessel whose capacity is V at C. 

1 c. c. dry air at a pressure of 76 cm. and at a temperature 
of C. weighs 0.001293 gramme. 

The weight of a given volume of any gas varies directly as 
the pressure and inversely as the temperature. 

The weight of V cubic centimetres of dry air at any tem- 
perature and at any pressure other than C. and 76 cm., 
respectively, would be calculated by the formula: 



22 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

If the change in temperature is great, the capacity of the 
glass vessel is altered, and allowance for this must be made. 

If the coefficient of expansion of the vessel is represented 
by Jc, then the preceding formula is changed to : 

W = 0.001293 - g ^~- t V(\ + tk). 

Should the weight of dry hydrogen be required instead 
of dry air, as here calculated, the value 0.0000896, the weight 
of 1 c. c. dry hydrogen at C. and at 76 cm., must be sub- 
stituted for the value 0.001293 in above formula. 

If the calculation is to be made by logarithms, the for- 
mula can be cast into the following form : 

For air : 
log. W= 7.6670 + log. H+ ar. co. log. (273 + t) 

-flog. F+log. (l + aO-20. 
For hydrogen : 
log. W= 6.5077 + log. H + ar. co. log. (273 + t) 

+ log. F+ log. (! + *&) -20. 

The constant in above formula, for air, viz., 7.6670, is thus 
obtained : 

The formula previously given contains the constant quanti- 

273 

ties 0.001293 -^. 
/b 

To abbreviate the calculation, the value for this expression 
has been figured as follows : 

log. 0.001293 = .111599 3 

log. 273 2.436163 

ar. co. log. 76 = 8.119186 - 10 

.666948 3 



3.666948 
+ 10.000000 

7.666948 (- 10.) 
which can be contracted to 7,6670 ( 10.) 



SPECIFIC GRAVITY. 23 

The value for hydrogen, 6.5077, is obtained in the same 
manner. 

The following will illustrate the calculation of a vapor 
density determination by Dumas' method: 

EXAMPLE: Calculate from the following data the specific gravity 
of camphor vapor referred to air as standard: 

"Weight of glass vessel a =50.134 grs. 

Height of barometer. . . H = 74.2 cm. 

Temperature t 13.5 C. 

"Weight of vessel aud vapor b =50.842 grs. 

Height of barometer H' = 74.2 cm. 

Temperature t' = 244 C. 

Volume . ... V - 295 c. c. 

Coefficient of expansion of glass k = 0.000025. 

As previously stated, specific gravity = * C ~ a . 

Calculation of c : 

Constant log. 7.6670 10. 

H= 74.2 log. 1.8704 

273 -f t = 286.5 ar. co. log. 7.5428 - 10. 

V= 295 log. 2.4698 

1.5500 
c = 0.3548 

Calculation of W: 

Constant log. 7.6670 10. 

H' = 74.2 log. 1.8704 

273 + t' = 517 ar. co. log. 7.2865 - 10. 

V= 295 log. 2.4698 

(1 + 244 X 0.000025) = 1.0061 log. 0.0025 

L2962 

b= 50.842 

c= 0.3548 

b+c= 51.1968 

a = 50.1340 

(6-fc-a)= .T0628 

Wlog. = 9.2962 

(b -f c - a) log. = 10.0265 

0.7303 
Number log. 0.7303 = 5.374 

Hence, specific gravity sought = 5.374 



24 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

II. Hofmann's Method. This method is particularly ap- 
plicable in dealing with substances of comparatively low boil- 
ing point. It bases on the observation of the volume and the 
tension of vapor produced from a weighed amount of sub- 
stance. 

The apparatus consists of a graduated glass tube,, which is 
first filled with mercury and then inverted over a mercury 
trough. The mercury on falling to its proper level, leaves a 
vacuous space in the upper part of the tube. This tube is 
jacketed by another tube of glass, so made that steam, or the 
vapor of some liquii boiling at a higher temperature than 
water, can be kept playing about the enclosed tube. 

A small quantity of the substance the vapor density of 
which is to be determined, is weighed off, passed up through 
the mercury and is thus introduced into the space above. 
There it vaporizes, and, in consequence of its tension, de- 
presses the mercury column. 

This depression of the mercury as well as the barometric 
pressure and the temperature obtaining at the time are 
noted, and these values, together with the weight of the 
substance taken, furnish all the data necessary for the calcu- 
lation. 

Referred to hydrogen as standard, the specific gravity of the 
vapor can be calculated by the formula : 



- w. 760. (1 + 0.00367 y) 

P ' v . 0.00008958 . (H - h) . (1 + kT) ' 



where w = weight of substance taken, and hence weight of 

vapor formed; 

v = observed volume of vapor expressed in cubic cen- 
timetres ; 

H reduced height of barometer at time of experi- 
ment ; 



SPECIFIC GRAVITY. 25 

h = reduced height of mercury in tube above that in 

trough; 

T temperature of vapor; 
lc coefficient of cubical expansion of glass. 

Or, calculation can be effected by the formula: Sp. Gr. = --, 

where IF' represents the weight of an equal volume of air, 
under conditions identical with those under which the volume 
of the vapor was determined. 

EXAMPLE : Calculate from the following data the specific gravity of 
chloroform vapor referred to air as standard : 

Weight of substance, and hence i w = Q 2500 gr. 

Weight of vapor ) * ' 

Volume of vapor V = 110 cc. 

Height of barometer H = 75.62 cm. 

Reduced height of mercury in tube 

above that in trough h = 32.25 cm. 

Temperature of vapor T = 100 C. 

Solving by means of logarithms, the value of IF' is found by 
the formula: 

log. FF= 7.6670 -f log. (Hh) + ar. co. log. (273 + t) -f log. V 
+ log. (1 + 1 0.000025) - 20. 

Constant log. 7.6670 10. 

H-h = 43.37 log. 1.6372 

273 -f t = 373 ar. co. log. 7.4283 - 10. 

F= 110 log. 2.0414 

(1 + 100 X .000025) log. 0.0008 

8.7747 - 10. 
w = 0.2500 log. 9.3979 - 10. 

0.6232 

Number log. 0.6232 = 4.20 
Hence, specific gravity of vapor sought = 4.20. 



26 LECTURE-XOTES ON THEORETICAL CHEMISTRY. 

III. Victor Meyer's Method. This method, which is equally 
well adapted for vapor-density determinations of substances 
with a high, as for those with a low, boiling-point, is the 
method now generally employed. 

A weighed amount of substance is vaporized in a vesse_ 
which contains air. 

The vapor displaces an equal volume of air, and this ex- 
pelled volume of air is measured. 

The apparatus consists of a jacketed glass cylinder of 
about 100 cubic centimetres capacity which opens into a nar- 
row glass tube that is provided with a well-fitting glass stop- 
per. A little below this stopper, a short branch-tube is 
attached, which leads into a water-trough and which termi- 
nates under a graduated glass vessel, an eudiometer, filled 
with water. 

To make a determination with this apparatus, the jacket 
surrounding the glass cylinder is filled with a liquid of known 
boiling-point. The liquid selected for this purpose of course 
has a boiling-point higher than that of the substance the 
vapor density of which is to be ascertained. 

A small amount of the substance to be examined is weighed 
out, placed into a small stoppered tube or bulb, and is intro- 
duced into the jacketed cylinder, where it is vaporized. The 
vapor produced expels an equal volume of air; this, in turn, 
displaces some of the water in the eudiometer, being itself 
thus confined and measured. 

The calculation is simple. The specific gravity of the 
vapor is equal to the weight of the vapor (the weight of the 
substance used), divided by the weight of an equal volume of 
air, i.e., by the weight of the air expelled. 

Expressed in a formula, taking air as standard, it would be : 



_ . .. 

0.0012937 v.(H-p) 



SPECIFIC GRAVITY. 27 

and, taking hydrogen as standard, 

_ w. (I 4- 0.00367 T) . 760 
bp< ~ 0.00008958 . v . (H - p)' 

in which formulae, 

w = weight of substance taken; 

v = the observed volume of displaced gas in cubic centi- 
metres; 

H = reduced height of barometer at time of experiment ; 

p = tension of aqueous vapor at the temperature of the 
measuring vessel. 

T = temperature of the water in the collecting trough. 

Calculation of determinations made by Victor Meyer's 
method, can of course also be effected by logarithms. 

The value sought, specific gravity referred to air as standard, 
can be calculated by the formula: 

log. Sp. Gr. = log. w log. w', 

where w = weight of vapor, 

to' = weight of displaced air, 

and where the value of log. w' is found by the expression, 

log. w' 
7.6670 - log. (H - p) -f ar. co. log. (273 + t) + log. V- 20. 

Or, the specific gravity can also be calculated by use of 
the following expression: 

log. Sp. Gr. = 2.3330 + ar. co. log. (H - p) 
4- log. (273 -f- t) + ar. co. log. F+ log. W 20. 

The value 2.3330 is obtained by subtracting the constant 
7,0670 from 10,0000, 



28 LECTUKE-KOTES ON THEORETICAL CHEMISTBY. 

EXAMPLE Calculate from the following data the specific gravity 
of carbon disulphide referred to air us standard: 

w= 0.0495 gr. 

*> = 16.4 c. c. 

H= 71.78 c. m. 

P = 1.40. 

T= 16.5 C. 

Log. Sp. Gr. = 2.3330 + ar. co. log. (Hp) -f- log. (273 -f t) 
-\- ar. co. log. v -f- log. w 20. 

23330 

(// - p) ar. co. log 8.1525 - 10 

(273 + log..., 2.4617 

ar. co. log. v 8.7852 10 

log.w 2.6946 

0.4270 

Number log. 0.4270 = 2.673. 
Hence, specific gravity of vapor = 2.673. 



CHEMICAL NOMENCLATURE AND NOTATION. 29 



CHAPTER III. 
CHEMICAL NOMENCLATURE AND NOTATION. 

THE development of the language of chemistry, condi- 
tioned as it has been by the evolution of the science, presents 
an interesting subject for study. 

Earliest Times. The oldest chemical terms were either very 
general, or else suggestive of the origin of the substances to 
which they were applied. 

Since the earliest times, the term " sal " has been used for 
everything having a salty taste; since the eighth century the 
kind or origin of the substance was indicated by an addi- 
tional word ; for instance, " sal maris." 

In Gebers writings there is no attempt at any system in 
the naming of chemical bodies; whether or not he was 
familiar with the use of any of the symbols for the metals 
which were used by the alchemists in later times, is very 
doubtful. They are certainly to be found in his works, but as 
these consist almost exclusively of Latin translations made in 
the sixteenth century, it is an open question whether they 
appeared in the original, or were inserted by the translators. 

Notation of the Alchemists. With the thirteenth century 
the alchemists commenced to use certain symbols quite freely. 

The seven metals, gold, silver, mercury, copper, iron, tin, 
lead, were known by the following names and symbols : 



Gold = Sol O 

Silver = Luna 3 

Mercury = Mercurius 9 
Copper = Venus 9 



Iron = Mars <j* 

Tin = Jupiter Qj. 
Lead = Saturnus 



30 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

Concerning the meaning of these symbols but little is 
known; the exact time when they were brought into use can 
also not be determined. 

It has been suggested that the symbol for Saturnus repre- 
sented his scythe, the symbol for Mars his shield and spear, 
the symbol for Venus her hand-mirror. Some of the 
alchemists believed that these symbols were indicative of 
the chemical peculiarities of the metals they represented. 
Thus the circle was regarded as illustrating perfection of the 
metallic state, the semicircle an approximation to this condi- 
tion, and so on. 

Since the thirteenth century the following signs were em- 
ployed to designate the four elements of Aristotle : 







Gradually other symbols found their way into alchemistical 
writings, but few of these met with general acceptance. 
Since the fourteenth century sulphur is quite generally found 
represented by the symbol ^. 

Attempts made in the period beginning with the thirteenth 
and extending to about the eighteenth century, to generalize 
terms of chemical substances, led to much trouble and con- 
fusion. 

The principal physical properties of substances were im- 
portant considerations in their naming. For instance, to 
everything fluid the term "mercurius" was given; pure 
mercury was " mercurius communis ;" alcohol was know T n as 
"mercurius vegetabilis." Viscous liquids received the ap- 
pellation "oleum;" thus, for instance, "oleum tartari" and 
" oleum vitrioli," to which latter term oil of vitriol is directly 
traceable. 

According to their different tastes, salts were distinguished 



CHEMICAL NOMENCLATURE AND NOTATION. 31 

as " salia acida " and " salia alcalina;" according to their 
volatility or non-volatility, they were divided into " salia 
alcalina fixa " and " salia alcalina volatilia." 

A yellow or yellowish-red metallic compound was called 
" crocus ;" a black compound was termed " aethiops." 

Nomenclature in the Seventeenth Century. In the seven- 
teenth century, when the number of compounds known in- 
creased rapidly, the names of the discoverers of these sub- 
stances were frequently used as an aid in distinguishing 
between them. The practice of having similar names indicate 
similarity of properties, originated only towards the end of 
this epoch. 

All sulphuric-acid salts were then designated as "vitriols;" 
nitric-acid salts came to be known as " salpetres." As a rule, 
similarity in terminology referred to the acid of the com- 
pound; salts consisting of the same base with different acids, 
were rarely indicated by similar-sounding names. 

In the beginning of the eighteenth century several at- 
tempts were made to introduce chemical signs and symbols 
which should express concisely the nature of substances. 

Geoffrey in 1718 used the customary symbols for the metals, 
and in addition introduced the following signs : 



Acids 
HC1. 



HNO, 




LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



Fixed Alkali 



Volatile Alkali... - 
Absorbing Earths = 



Phlogiston 
Principe huileux 
Soufre principe 




X / 



Vinegar , 



Salt 



Alcohol. 




Bergman's System. About the middle of the eighteenth 
century Macquer and Baume strongly emphasized the neces- 
sity of designating substances similar in composition, by similar 
names. Their efforts were supported in 1770 by Bergman, 
who advocated a new system of nomenclature, based however, 
as far as possible, on the terms then in vogue. He made 
various suggestions as to how this could be accomplished, but 
was himself not very consistent in the adoption and use of 
these terms. 

In 1780 Bergman also proposed to use similar symbols for 
bodies analogous in composition, each body to be designated 
by some specific symbol. 



CHEMICAL NOMENCLATURE AND NOTATION. 33 

The four elements and the two combustible bodies, sulphur 
and phosphorus, were to be indicated by triangles drawn in 
different ways. Metallic bodies (regulos) were to be repre- 
sented by a crown ; a circle was to denote salts and alkalies, a 
cross the acids. 

To Bergman is also due the first attempt to use compound 
symbols which were intended to indicate the nature of chemi- 
cal combinations. 

The compound salts were to be expressed by the name of 
the alkali which they contained, together with an adjective 
formed from the name of the acid. The following will 
explain : 

Modern Symbols. Bergman's Appellation. 

K 2 S0 4 Alkali vegetabile vitriolatum. 

Na 2 S0 4 Alkali fossile vitriolatum. 

(NH 4 ) 2 S0 4 Alkali volatile vitriolatum. 

KN0 3 Alkali vegetabile nitratum. 

NaN0 3 Alkali fossile nitratum. 

NaCl Alkali fossile salitum. 

Etc., etc. 



Black's List of Synonyms. That endless confusion reigned 
in the matter of chemical nomenclature by this time, and 
how pressing was the need of reform, is most strikingly shown 
by the list of the "most usual synonimes" given in Dr. 
Joseph Black's " Lectures on the Elements of Chemistry, 
etc.," Vol. II. p. 148 (first American from the last London 
edition, 1806, Philadelphia). 

The following are the synonyms there given for potas- 
sium, sodium, and ammonium. The other substances enu- 
merated in Black's list, rejoice in from two to eleven synonyms 
each. 



34 



LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



SALIUM ALKALINORUM SYNONIMA. 



Potassium. 

1. Lixiva. 

2. Alkali fixum vegetabile. 

3. Kali. Pharm. Lond. 

4. Potassa. Gallis. 

5. Sal tartari. 

6. Sal absynthii. 

7. Cineres clarellati. Nitrum 

fixatum. 

8. Oleum tartari. 

9. Lixivium tartari. 
10. Aqua kali. Lond. 

Sodium. 

1. Trona. 

2. Alkali fixum fossile. 

3. Soda. Pharm. Edin. 



4. Natron. Lond. 

5. Soda. Gallis. 

Ammonium. 

1. Ammonia. 

2. Alkali volatile. Edin. 

3. Ammonia. Lond. 

4. Ammoniaca. Gallis. 

5. Sal volatile ammoniaci. 

6. Sal cornu cervi. 

7. Sal urinae. 

Aqua dilutum. 

8. Spirit us salis ammoniaci. 

9. Aqua ammoniae. 

10. Spiritus cornu cervi. 

11. Spiritus urinae. 



French Systems of Nomenclature. The system of Bergman 
met with quite universal favor; but when the phlogiston 
theory was overthrown and Lavoisier's dualistic theory 
carried the field, a new system of nomenclature became 
imperative. 

The method proposed by Bergman, to have the nomen- 
clature reduced to some system valid for the whole of 
chemical science, and which system should be applicable 
to each and every new addition to the science, was retained, 
while the construction of the nomenclature was changed 
so as to meet the wants of the newly-formed " French Chem- 
istry." 

In 1782 Guyton de Morveau published in the Journal de 



CHEMICAL NOMENCLATURE AND NOTATION. 35 

Physique an outline of a system of chemical nomenclature. 
This was based on the phlogiston theory, but bore in it some 
of the features which are retained in the system used at the 
present time. 

De Morveau distinguished clearly between acids, bases, 
and salts. The acids all received the term " acides " and were 
distinguished from one another by adjectives which indicated 
the kind of acid; for instance, acide vitriolique, acide nitreux, 
acide oxalique, etc. 

The salts were named from the acid and the base that 
formed them; for instance, vitriol de cuivre, fleur de calce, 
nitre de mercure. Among the bases he counted the metals, 
alcohol, and phlogiston. 

In 1787 Lavoisier, Morveau, Berthollet, and Fourcroy pre- 
sented to the French Academy a detailed plan of a new 
system of nomenclature. This memoir was entitled " Methode 
de Nomenclature Chimique. Proposee par MM. de Morveau, 
Lavoisier, Berthollet, et De Fourcroy/' and was published 
in Paris in 1787, " Sous le Privilege de PAcademie des 
Sciences." 

The elements, or, as the authors call them, simple sub- 
stances, " those which up to the present time have not been 
decomposed," are divided into five classes. 

Class I. "embraces those bodies [principes] which, with- 
out exhibiting among themselves a well-marked analogy, 
have nevertheless this in common, that they seem preferably 
to approach the elementary condition \Vetat de simplicite] 
which causes them to resist analysis and at the same time 
renders them so active in combinations." 

This class consists of five bodies: light (la htmiere), heat- 
matter (la matiere de la chaleur), dephlogisticated or vital air 
(I' air appele d'abord deplilogistique, puis air vital), inflam- 
mable gas (le gaz inflammable), and phlogisticated air (I'air 
plilogistique). 



36 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

To these substances the memoir assigns the following 
names : 

lumiere = lumiere. 

matiere de la chaleur = calorique. 

Fair dephlogistique, air vital = oxigene. 
gaz inflammable = hidrogene. 

Fair phlogistique = azote, from the Greek a (no) 

and CGorf (life). 



Class II. " All acidifiable bases or radical principles of the 
acids." 

Among these were classed nitrogen, carbon, sulphur, 
phosphorus, the " muriatic " radical, the " boracic " radical, 
etc. This class embraces twenty-six bodies, again including 
nitrogen. 

Class III. consists of those bodies " the principal charac- 
teristic of which is to exhibit the metallic condition." This 
class contains seventeen bodies. Among these are named: 
arsenic, molybdenum, tungsten, manganese, nickel, cobalt, 
bismuth, antimony, platinum, and gold. 

Class IV. is assigned to the five earths, which are enu- 
merated as follows : la silico, 1'alumine, la baryte, la chaux, 
la magnesie. Class V. consists of the three alkalies, potas- 
sium, sodium, ammonium. 

In addition to these five classes, an appendix is provided 
which contains "those more compound substances which 
combine in the manner in which the elements combine, or 
without undergoing sensible decomposition." 

This appendix contains seventeen divisions, and among the 
substances enumerated are mucilage, gluten, sugar, starch, 
resin, alcohol, ethers, and soaps. 

It was the aim of those who proposed this system of nomen- 
clature that the names given to compounds should : 
indicate the body, 
define it, 



CHEMICAL NOMENCLATURE AND NOTATION. 37 

recall its constituent parts, 

classify it according to its composition, 

indicate, in a manner, the relative proportion of its 

constituents. 

Thus, for instance, to quote an example given in this 
memoir: 

Sulphuric acid is to designate sulphur saturated to its 

utmost with oxygen. 
Sulphurous acid is to represent sulphur joined to a less 

amount of oxygen. 

Sulphate is to be the name of all salts formed from sul- 
phuric acid. 

Sulphite is to be the name of all salts formed from sul- 
phurous acid. 

Sulphide is to indicate all combinations of sulphur 
not brought to the acid state (i.e., not combined with 
oxygen). 

This will suffice to give an idea of how much the chemical 
nomenclature of to-day owes to the labors of Lavoisier, De 
Morveau, and their associates. 

This publication contains also a most valuable " Synonimie 
ancienne et nouvelle par ordre alphabetique," and a " Dic- 
tionnaire pour la nouvelle Nomenclature Chimique." 

Symbols of Hassenfratz and Adet. Appended to this work 
and indorsed by its authors, is given a system of chemical 
symbols by Hassenfratz and Adet, of course adapted to the 
anti-phlogistic theory. 

The elementary bodies are represented by simple symbols; 
the metals, for instance, by circles into which the first letter 
of their Latin name is placed, to distinguish them one from 
the other. All alkalies and earths are indicated by triangles 
placed in different positions. 

Oxygen, nitrogen, hydrogen, etc., are denoted by lines, 
straight or curved. 



38 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

The following are a few of the symbols employed : 



7 3 C 



OXYGEN HITROGEN HYDROGEN CARBON SULPHUR ^HOSPHQRUS 

W A0 O 

CALCIUM BARIUM 8O DA COPPER LEAD SILVER 
EARTH EARTH 



Compounds are indicated by combinations of symbols like 
the above. For instance : 




PHOSPHATE OF CALCIUM 



The authors of this system also attempted to depict by 
their symbols differences in the constitution of compounds 
formed from the same constituents. This they sought to 
accomplish by the position which the several symbols were 
made to occupy relatively to each other. For instance, the 
following was intended to indicate the different steps of 
oxidation of nitrogen to nitric acid : 



Other Systems Proposed. The system of nomenclature of 
Lavoisier, De Morveau, and their colleagues, was appreciated 



CHEMICAL NOMENCLATURE AND NOTATION. 39 

and adopted by many chemists in France and in other 
countries; but opponents to it were also not lacking. 

The adherents of the phlogiston theory naturally opposed 
it; but even others, among them Sir Humphry Davy, did not 
favor its acceptance. The latter made some suggestions con- 
cerning the subject, which suggestions however, did not find 
general approval. 

It is not feasible to enumerate in detail the various propo- 
sitions that were made in this connection, from all sides. As 
Dr. Black stated in his " Lectures on Chemistry/ 7 previously 
cited: "When this rage for reformation and unioration was 
going round it was natural for every person to think a little 
on the subject, and consider what he would propose were it 
required of him to give his opinion." 

Thomson in 1804 suggested that the different stages of 
oxidation be denoted by prefixes; e.g., protoxyd, deutoxyd, 
peroxyd, etc. 

One attempt was made, some years later, to create a 
chemical nomenclature to be used by all nations of Germanic 
descent. 

Oxygen was to be known as " Eld " (from the Danish lid, 
i.e., fire). " Eldluft " represented oxygen-gas ; " Elden " meant 
to oxidize. Hydrogen was termed " Brint " (derived from 
brennen, to burn); alkali was denoted by the word " Aesch;" 
etc. 

In 1808 Dalton published his " New System of Chemical 
Philosophy." In this he represents the atoms of the different 
elements by circles, and these circles are provided with some 
distinguishing mark. 

He conceived the atoms as being spheriform, and in this 
respect his system differs from that of Hassenfratz and Adet, 
who had reserved the circle as a symbol for the metals, with- 
out, however, intending to convey thereby an-y notion as to the 
configuration of the atoms. All of Dalton's circles did not 
bear the initial pf the name of the element to be represented; 



40 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

instead, he used in many instances dots and lines, as the fol- 
lowing symbols show : 








CARBON 








He, moreover, assigned to each symbol the duty of repre- 
senting the weight of the element, according to a table of 
atomic weights which he published in this work. 

He chose hydrogen as unit, nitrogen = 5, carbon = 5, oxy- 
gen = 7, sulphur = 13, and so on. 

His symbols of compounds therefore not only indicated the 
elements of which the compounds consisted, but illustrated 
as well, according to his views, their quantitative composi- 
tion. The following represent respectively : 

WATER. AMMONIA. NITRIC ACID. 

0O 00 



In 1811 Berzelius published in the Journal de Physique 
an article which explained his views concerning chemical 
nomenclature. His scheme rested to a great extent on the 
system published by Lavoisier and his colleagues, and was 



CHEMICAL NOMENCLATURE AND NOTATION. 41 

originally expressed in the Latin language. It is the system 
essentially yet in vogue at the present day. 

His system of notation permitted of the writing of chem- 
ical formulae, which came into use in 1815. The abbreviated 
mineralogical formula had already been introduced by him 
in 1814. 

The use of the symbols of Berzelius is retained to the present 
day ; the initial, or the initial and the following, or, the initial 
and the last letter, of the name of an element, denote the 
element. 

In his mineralogical formulae Berzelius indicated the num- 
ber of atoms of oxygen by a corresponding number of dots 
placed over the letters ; a bar drawn through the letter or 
letters indicated two atoms of the element designated. Thus : 

-hi = Cu 2 0, Cuprous oxide. 
Pb = Pb(X , Plumbic oxide. 
CaC = CaO,C0 2 , Calcic carbonate. 

System of the Present. At the present time there is still 
considerable diversity of opinion concerning chemical nomen- 
clature. Within the past decade, and especially quite re- 
cently, several important attempts have been made to bring 
about a thorough reform in these matters, and these efforts, it 
is to be hoped, will ultimately lead to the universal acceptance 
by all nations of some one system of chemical nomenclature 
and notation.* 

The principles of nomenclature which follow below, in 
broad outline, are those now quite generally accepted. 

* See Proceedings of International Commission for the Reform of 
Chemical Nomenclature, Geneva, 1892. 

Le Moniteur Scientifique, Dr. Quesneville, 1892, p. 401. The Chem- 
ical News, vol. 65, p. 277, 



42 LECTUKE-NOTES ON THEORETICAL CHEMISTRY. 

NAMES AND SYMBOLS OF THE ELEMENTS. The few ele- 
ments which were known to the ancients, retain their appel- 
lation of old; the names of the elements more recently 
found, have been given by their discoverers without conformity 
to any rule or regulation, excepting, that if the element is a 
metal its name receives the termination urn, if a non-metal, 
the termination ine, on, or gen. 

Some elements have received the name of a country, like 
Columbium, Gallium, Germanium. In other instances they 
have been named from some deity; thus, Thorium is derived 
from Thor, the Norse god; Tantalum recalls a figure of Greek 
mythology. 

Frequently some characteristic property of the element has 
suggested the name which it received. Thus, Iodine is derived 
from the Greek iov 9 a violet; Iridium, from the Latin iris, 
rainbow; Barium from the Greek fiapvs, heavy. 

At times the planets have been selected as sponsors, as in 
the case of Mercury; Tellurium is named from the Latin tellus, 
the earth, and Selenium from the Greek creA 77^77, the moon. 

The symbols of the elements are abbreviated designations 
of their names. These symbols consist of the first, or of the 
first and some one additional letter of the Latin, or other, 
name of the element; thus, 0, represents carbon: Co, cobalt; 
and Cu, copper, this last symbol being derived from the 
Latin word cuprum. 

The symbol of an element stands not only for the name of 
that element, but represents a definite amount of the same 
one atom. If more than one atom is to be indicated, the re- 
quired numeral is placed with the symbol, either before it, or 
else immediately after and a little below the symbol. This 
same plan is followed in expressing the composition of com- 
pounds. 

NAMES OF COMPOUNDS. The names of compounds are in- , 
tended to express, as far as possible, the constitution of the 
substance. 



CHEMICAL NOMENCLATURE AXD NOTATION. 43 

If the compound consists of only one metal and one non- 
metal, the non-metal, receiving the termination ide furnishes 
the group name, and the metal the specific name. Thus, all 
compounds of metals with chlorine alone, are termed chlo- 
rides; all compounds of metals with sulphur alone, sulphides; 
but sodium chloride and silver sulphide denote, respectively, 
but one particular compound. 

If two elements combine with each other in two different 
proportions, the termination ic is given to the name of the 
metal in that combination which contains most of the non- 
metal, and the termination ous is given to the name of the 
metal in that combination which contains least of the non- 
metal. 

Thus, Cu 2 is cuprous oxide, and CuO is cupric oxide. In 
the latter, one atom of oxygen is combined with one atom of 
copper; in the former, there is but one half as much oxygen 
for each atom of copper present. If the ratio of two ele- 
ments is as 1 : 1, the term sesqui is used to denote this 
relation. Thus : 

FeCl. 2 = ferrous chloride; 
Fe 2 Cl 6 = sesquichloride of iron ; usually termed, 
ferric chloride. 

If a given amount of one element forms se\eral combina- 
tions with some other element, Latin or Greek numerical 
prefixes are employed to distinguish the compounds. Thus: 

N 2 = nitrogen monoxide; 
N 2 2 = " dioxide; 
N a 3 = " trioxide; 
N 2 4 = " tetroxide; 
N 3 5 = " pentoxide. 

The terminations ic and ous are also used to distinguish 
acids consisting of the same elements, but containing these 
elements in different proportions. If combinations of the 



44 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

same elements exist in more than two proportions, use is 
made of Latin or Greek prefixes in addition to employing the 
endings ic and ous. Thus : 

HC10 = * hypochlorous acid ; 

HC10 3 = chlorous acid; 

HC10 3 = chloric acid; 

HC10 4 = f perchloric acid. 

Salts formed from ic acids receive the termination ate. 
Salts formed from ous acids receive the termination ite. 
Salts of hypo- and per- acids retain these prefixes, but 
otherwise obey the rule just stated. 

Thus, the sodium salts of the acids above enumerated, are: 

NaCIO = sodium hypochlorite; 
NaC10 2 = " chlorite; 
NaC10 3 = " chlorate; 
NaC10 4 = '" perchlorate. 

Among other prefixes occasionally employed there should 
be noted : met a, signifying " near to ;" para., signifying 
"equal;" sub, signifying that the compound, to the name of 
which this word is prefixed, contains less of a constituent 
than the name otherwise implies. Thus, cuprous oxide, Cu 2 0, 
was formerly termed suboxide of copper, to distinguish it 
from CuO, which was known as the oxide of copper. 

The intention of having the name of a substance indicate 
its composition has received its widest application in the 
chemistry of the carbon compounds. 

Thus, von Hoffmann proposed the following scheme for the 
naming of the hydrocarbon series : 

All members of the C n II 2n+2 series receive names terminat- 



* From vTto, under. f From vrcep, over. 



CHEMICAL NOMEKCLATtJUE AND 



45 



ing in cine ; all of the series C n H 2jl have names ending in 
ene; those of the C n H 2n _ 2 series bear the ending ine, of the 
C n H 2n _4 series, the ending one, and of the C n H 2n -e series, the 
ending une. 

Furthermore, with the exception of the first four members 
of the series, which are allowed to retain their original, arbi- 
trary, appellations, the Latin numeral which indicates the 
number of carbon atoms in the compound, determines the 
name of the compound, as the following list shows : 



C n H 2n +2 


CuH 2n 




CnH 2n -2 


Methane. . . CH 4 


Methene . . 


CH, 




Ethane.... C,H 8 


Ethene . . 


C.H. 


Ethine .... C 2 H a 


Propane. . .C S H 8 


Propeue. . . 


C,H. 


Propine. . ..C 3 H 4 


Butane . . C H 


Butene 


.C H 


Butine ..C H 






^48 




Pentane ,..C 5 H 12 


Pentene . . 


C.H,. 


Pentine. . . . C 6 H 8 


Hexane C H 4 


Hexene . . . 


..C H 


Hexine C H 


Heptane... C 7 H 16 


Heptene. . 


0,H,. 


Heptine...C,H ls 


Octane C H 


Octene. . . 


.C H 


Octine C H 










C n H 2 n-4 


C,,H 2n _ 


-6 




Propone. . .C 3 H 2 








Butone C 4 H 4 


Butune . . . 


. C 4 H 2 





Pentone. ..C 6 H 6 


Pentune . . 


.C 5 H 4 




Hexone. . ..C 6 H 8 


Hexune . 


.C 6 H 8 




Heptone.. ,C 7 H 10 


Heptune. . 


.C.H 8 




Octone....C & H 12 


Octune. . . 


C 8 H 10 






American Spelling and Pronunciation of Chemical Terms. 
In view of the great importance attaching to the mat- 
ter, it seems desirable to reproduce here a complete 



46 LECTURE-NOTES ON" THEORETICAL CHEMISTRY. 

summary of the rules for the spelling and the pronunciation 
of chemical terms that were adopted by the American Asso- 
ciation for the Advancement of Science in 1891. 

This summary has been arranged in the form of a chart 
that is issued by the Bureau of Education, Department of the 
Interior, Washington, D. C., for general distribution to high 
schools and colleges, and following is an authorized tran- 
script of its contents : 

In 1887 a committee was appointed by the American As- 
sociation for the Advancement of Science to consider the 
question of attaining uniformity in the spelling and pronun- 
ciation of chemical terms. The work of this committee 
extended through the following four years. As a result of 
widespread correspondence and detailed discussion at the 
annual meetings of the Chemical Section of the American 
Association, the accompanying rules have been formulated 
and adopted by the Association. They are submitted to 
chemists generally, and especially to the large number of 
those engaged in teaching chemistry, with the request that a 
cordial and earnest effort be made to render their use general 
and thus obviate the many difficulties arising from the present 
diversities of style. 

T. H. NORTON, Ph.D., 

Professor of Chemistry, University of Cincinnati 

EDWARD HART, Ph.D., 
Professor of Chemistry, Lafayette College, Easton, Pa. 

H. CARRINGTOST BOLTON, Ph.D., 

University Club, New York City. 

JAS. LEWIS HOWE, Ph.D., M.D., 

Polytechnic Sociely, Louisville, Ky. 

Committee. 

General Principles of Pronunciation. 1. The pronunciation 
is as much in accord with the analogy of the English lan- 
guage as possible. 



CHEMICAL NOMENCLATURE AND NOTATION. 4? 

2. Derivatives retain as far as possible the accent and pro- 
nunciation of the root word. 

3. Distinctly chemical compound words retain the accent 
and pronunciation of each portion. 

4. Similarly sounding endings for dissimilar compounds are 
avoided (hence -id, -ite). 

Accent. In polysyllabic chemical words the accent is 
generally on the antepenult; in words where the vowel of the 
penult is followed by two consonants, and in all words end- 
ing in -ic, the accent is on the penult. 

Prefixes. All prefixes in strictly chemical words are re- 
garded as parts of compound words, and retain their own 
pronunciation unchanged (as, a'ceto-, a'mido-, a'zo-, hy'dro-, 
I'so-, ni'tro-, nitro'so-). 

Elements. In words ending in -ium, the vowel of the ante- 
penult is short if i (as,.Iri'dium), or y (as, didj'mium), or if 
before two consonants (as, ca'lcium), but long otherwise (as, 
tlta'nium, sele'nium, chro'mium). 

alu'minum co'pper magne'sium (zhium) 

a'ntimony didy'mium ma'nganese (eze) 

a'rsenic e'rbium me'rcury 

bfi'rium flii'orin muly'bdenum 

bi'smuth (biz) gallium ni'ckel 

bo'ron germa'nium ni'trogen 

bro'mm glu'cinum 6'smium 

ca'dmium gold 6'xygen 

cri'lcium hy'drogen pallfi'dium 

ca'rbon i'ndium phos'phorus 

ce'rium I'odin pla'tinum 

ce'sium irl'dium pota'ssium 

chlo'rin iron rho'dium 

chro'mium la'nthanum rubi'dium 

co'balt lead ruthe'nium 

colu'mbium li'thium 



4S LECTITRE-KOTES Otf THEORETICAL CHEMISTRY. 

sca'ndium ta'ntalum tu'ngsten 

sele'nium tellu'rium ura'nium 

si'licon te'rbium vana'dium 

silver tha'llium ytte'rbium 

so'dium tho'rium y'ttrium 

stro'ntium (shium) tin zinc 

su'lfur titii'nium zirco'nium 

Also: ammd'nium, phospho'nium, hiVlogen, cya'nogen, 
ami'dogen. 

Note in the above list the spelling of the halogens, cesium 
and sulfur; f is used in the place of ph in all derivatives of 
sulfur (as, sulfuric, sulfite, sulfo-, etc.). 

Terminations in -ic. The vowel of the penult in polysyl- 
lables is short (as, cya'nic, fuma'ric, arse'nic, sili'cic, id'dic, 
buty'ric), except (1) u when not used before two consonants 
(as, mercu'ric, pru'ssic), and (2) when the penult ends in a 
vowel (as, benzo'ic, ole'ic) ; in dissyllables it is long except 
before two consonants (as, bo'ric, ci'tric). Exception : ace'- 
tic or ac6'tic. 

The termination -ic is used for metals only where neces- 
sary to contrast with -ous (thus avoid aluminic, ammonic, 
etc.). 

Terminations in -ous. The accent follows the general rule 
(as, pla'tinous, su'lfurous, pho'sphorous, coba'ltous). Excep- 
tion: ace'tous. 

Terminations in -ate and -ite. The accent follows the gen- 
eral rule (as, a/cetate, va'nadiite). In the following words the 
accent is thrown back: a/bietate, a'lcohohite, a'cetonate, 
a/ntimonlte. 

Terminations in -id (formerly -ide). The final e is dropped 
in every case and the syllable pronounced id (as, chlo'rid, 
I'odld, hy'drid, 6'xid, hydro'xid, su'lfid, a'mid, a'nilid, 
mure'xid). 



CHEMICAL NOMENCLATURE AND NOTATION. 49 

Terminations in -ane, -ene, -ine, and -one. The vowel of 
these syllables is invariably long (as, me'thane, 6'thane,na'ph- 
thalene, a'nthracene, pro'pme, qui'none, a'cetone, ke'tone). 

A few dissyllables have no distinct accent (as, benzene, 
xylene, cetene). 

The termination -ine is used only in the case of doubly un- 
saturated hydrocarbons, according to Hofmann's grouping 
(as, proplne). 

Terminations in -in. In names of chemical elements and 
compounds of this class, which includes all those formerly 
ending in -ine (except doubly unsaturated hydrocarbons), the 
final e is dropped, and the syllable pronounced -in (as, chlo'rin, 
bro'min, etc., a 'mm, a'nilm, mo'rphm, qui'nm (kwi'nin), 
vanl'UIn, alloxa'ntm, absi'nthin, emu'lsm, caffein, co'cain). 

Terminations in -ol. This termination, in the case of spe- 
cific chemical compounds, is used exclusively for alcohols, and 
when so used is never followed by a final e. The last syllable 
is pronounced -61 (as, gly'col, phe'nol, cre'sol, thy'mol (ti), 
gly'cerol, qui'nol). Exceptions : alcohol, a'rgol. 

Terminations in -ole. This termination is always pro- 
nounced -ole, and its use is limited to compounds which are 
not alcohols (as, i'ndole). 

Terminations in -yl. No final e is used; the syllable is 
pronounced yl (as, a'cetyl, a'myl, ce'rotjfl, ce'tyl, e'thyl). 

Terminations in -yde. The y is long (as, a'ldehyde). 

Terminations in -meter. The accent follows the general 
rule (as, hydro 'meter, baro'meter, lacto'meter). Exception: 
words of this class used in the metric system are regarded as 
compound words, and each portion retains its own accent (as, 
ce'ntime"ter, mi'llime"ter, ki'lome"ter). 

Miscellaneous Words which do not fall under the preced- 
ing rules. 

Note the spelling : 

albumen albuminiferous gramme 

albuminous asbestos radical 



50 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

Note the pronunciation : 

a'lkalme centigrade no'mencla/'ture 

a'lloy (n. & v.) concentrated ole'fiant 

a'llotropy crystallin or crystal- va'lence 

a'llotropism line u'niva/'lent 

I'somerisni electro'lysis bi'va"lent 

po'lymerism liter tri'va/'lent 

appara'tus (sing. & plu.) mo'lecule qua'driva"lent 

aqua regia mole'cular ti'trate 

bary'ta 

A List of Words whose Use should be Avoided in Favor of 
the Accompanying Synonyms. 

For Use 

sodic, calcic, zincic, nickelic, ( sodium > ^^ zinc ' ni / cke ? 1 ' 

etc., eWorld, etc. j etc " chlond ' etc ' < VM ?' 

terminations in -ic, supra). 

arsenetted hydrogen arsin 

antimonetted hydrogen stibin 

phosphoretted hydrogen phosphin 

sulfuretted hydrogen, etc. . . hydrogen sulfid, etc. 

beryllium glucinum 

niobium columbium 

glycerin glycerol 

hydroquinone (and hydrochi- 

non) quinol 

pyrocatechin catechol 

resorcin, etc resorcinol, etc. 

mannite mannitol 

dulcite, etc dulcitol, etc. 

benzol benzene 

toluol, etc toluene, etc. 

thein caffein 

furfurol furfuraldehyde 

fucusol fucusaldehyde 



CHEMICAL NOMENCLATURE AND NOTATION. 51 

For Use 

anisol methyl phenate 

phenetol ethyl phenate 

anethol methyl allylphenol 

alkylogens alkyl haloids 

titer (n.) strength or standard 

titer (v.) titrate 

monovalent univalent 

divalent, etc bivalent, etc. 

quantivalence valence 

Fate, fat, far, mete, met, pine, pin, marine, note, n6t, 
move, tube, tub, rule, my, y = i. 

' Primary accent; " secondary accent. 

N.B. The accent follows the vowel of the syllable upon 
which the stress falls, but does not indicate the division of 
the word into syllables. 



52 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



CHAPTER IV. 
ATOMS, ATOMIC MASS, VALENCE. 

Introductory. Lavoisier was the first to recognize the fact 
that the elements combine in definite mass-proportions. 

Proust, another French chemist, was the first to prove that 
the elements combine in a small number of definite fixed pro- 
portions, but he did not succeed in giving a correct explana- 
tion of chemical combination. 

John Dalton's investigations led him, independently of the 
work of others, to the discovery of the law of combination in 
multiple proportions. 

Laws of Chemical Combination. The two important laws 
of chemical combination can be thus stated: 

LAW or DEFINITE PROPORTIONS: Chemical combination 
always takes place between definite masses (weights) of sub- 
stances. 

LAW OF MULTIPLE PROPORTIONS: If two elements com- 
bine in different proportions, the relative amounts of the one 
which combine with a fixed amount of the other are simple 
multiples of each other. In order to explain these facts, 
Dalton advanced his famous Atomic Theory. 

Two hypotheses concerning the constitution of all ele- 
mentary forms of matter present themselves for considera- 
tion. 

Matter is either infinitely divisible, or it is not infinitely 
divisible. 

Concerning the former hypothesis this, from its very 
nature, is incapable of direct proof or demonstration, and 
must always remain solely a subject for speculation. 



ATOMS, ATOMIC MASS, VALENCE. 53 

Acceptance of the second hypothesis involv-es of necessity 
the assumption of the existence of ultimate, indivisible par- 
ticles of matter. Such particles are termed atoms, from the 
Greek aro/fos, signifying indivisible. 

Dalton conceived the idea that there might be some con- 
nection between the laws of fixed and multiple proportions, 
and the hypothesis that matter consists of indivisible par- 
ticles, atoms. 

Atomic Mass. One universal property of matter is mass 
(weight). As atoms are assumed to be the ultimate ^articles 
of matter, atoms must be possessed of mass (weight). 

As the different fundamental forms of matter, the so-called 
elements, differ from one another in their mass, it is only 
reasonable to suppose that the very atoms of the elements 
differ from one another in this respect. 

It is assumed whenever chemical combination occurs be- 
tween two elements, that the union takes place between the 
atoms of these elements. 

In case an equal number of atoms of two elements, A and 
B, are allowed to enter into chemical combination, a new 
substance will be formed as the result of such union, and, 
providing that said elements combine with each other atom 
for atom, no trace will be left of either of the constituents A 
and B. 

If the mass of an atom of .4 is 1, and the mass of an atom 
of B is 15, then, as A and B are supposed to combine atom 
for atom, the resulting compound would contain A and B 
in the proportion of one part by weight of A to fifteen parts 
by weight of B. 

If therefore, on analysis, a compound is found to contain 
one part by weight of one element to, say, fifteen parts by 
weight of another, the inference might be drawn that the 
masses of the atoms of these elements bear to each other the 
ratio of 1 : 15, an inference which does not necessarily follow. 

Assuming matter to consist of atoms, and assuming chem- 



54 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

ical action to take place between atoms, it is evident why 
chemical action always takes place between definite amounts 
by weight, and there is thus gained a feasible explanation of 
the law of combination in definite proportions. 

Furthermore, it follows, as atoms are indivisible, that if 
elements combine with one another in more than one propor- 
tion, the proportions in which they combine must necessarily 
be a very simple one ; for instance, as 1 : 1, as 1 : 2, as 1 : 3, and 
so on. 

This would fully explain the law of combination in multi- 
ple proportions. 

Standards of Atomic Mass. The atom is the smallest mass 
of an element which can enter into chemical combination. 

The atomic mass of an element is the relative mass of an 
atom of that element, referred to the mass of an atom of 
some other element taken as unity. 

The selection of an element as standard of atomic mass 
presents considerable difficulty. 

Hydrogen was selected by Dalton as his standard, and it is 
the unit of atomic masses still generally used, because hydro- 
gen enters into chemical combinations in smaller proportion 
by weight than any other element. 

Berzelius adopted oxygen as standard, calling 100. 

As the atomic masses of many elements can be determined 
directly with reference to oxygen, some eminent chemists have 
lately again urged the adoption of oxygen as the standard, 
making = 16. This would assign to hydrogen an atomic 
mass of from 1.003 (Ostwald) to 1.007 (Clarke), according to 
some of the most recent and exact investigations. 

The atomic mass values in the first column, with = 16, 
are taken from a table revised by F. W. Clarke, October, 
1891; the values in the second column, with H 1, are taken 
from A. Rossing, Einf iihrung in das Studium der theoretischen 
Chemie, 1890. 



ATOMS, ATOMIC MASS, VALENCE. 

Table of Atomic Masses. 



55 



Name. 


Symbol. 


Atomic Mass, 
= 16. 


Atomic Mass, 
H = l. 


Aluminum 


Al 


27 


2704 


Antimony 


Sb 


120. 


119.6 


Arseuic 


As 


75. 


74.9 


Barium .... 


Ba 


187 


1369 


Bismuth 


Bi 


208.9 


207.3 


Boron 


B 


11 


109 


Bromine 


Br 


79.95 


79.75 


Cadmium 


Cd 


112. 


111.7 


C&sium 


Cs 


132 9 


132 7 


Calcium . ... ... 


Ca 


40 


39 91 


Carbon 


C 


12. 


11.97 


Cerium 


Ce 


140 2 


139 9 


Chlorine 


Cl 


3545 


35.37 


Chromium 


Cr 


52 1 


524 


Cobalt . ... 


Co 


59 


58 6 


Columbium 


Cb 


94 


93 7 


Copper . 


Cu 


63 6 


63 18 


Erbium 


Er 


166 3 


166. 


Fluorine 


F 


19. 


19 1 


Gadolinium 


Gd 


156 1 




Gallium 


Ga 


69 


699 


Germanium 


Ge 


72.3 


723 


Glucinum 


Gl 


9 


9 08 


Gold 


Au 


1973 


196 7 


Hydrogen 


H 


1.007 


1 


Indium 


In 


113.7 


113.6 


Iodine 


I 


126 85 


126 54 


Iridium 


Ir 


193.1 


192 5 


Iron 


Fe 


56. 


55.88 


Lanthanum 


La 


1382 


138 


Lead .... 


Pb 


206 95 


2064 


Lithium 


Li 


7.02 


701 


jVIafiruesium . . .... 


Mg 


24 3 


24 30 


jManganese 


Mn 


55. 


54 8 


jMercurv 


Hg 


200 


199 8 


Molybdenum 


Mo 


96 


959 


Xeodymium 


Nd 


140.5 




Nickel 


Ni 


58 7 


58 6 


^Nitro r en . 


N 


1403 


14 01 




Os 


190.8 


191 


Oxvtren 


O 


16 


15 96 


Palladium . . ... 


Pd 


106 6 


106 2 











LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

TABLE OF ATOMIC MASSES. Continued. 



Name. 


Symbol. 


Atomic Mass, 
O ^ 16. 


Atomic Mass, 
H = 1. 


Phosphorus 


P 


81. 


30.96 


Platinum 


Pt 


195. 


194.3 


Potassium 


K 


39.11 


39.03 


Praseodymium 


Pr 


143.5 




Rhodium 


Rh 


103. 


104.1 


Rubidium . 


Rb 


85.5 


85.2 


Ruthenium ... 


Ru 


101.6 


103.5 


Samarium 


Sm 


150. 


150. 


Scandium 


Sc 


44. 


43.97 


Selenium . . 


Se 


79. 


79.0 


Silicon 


Si 


28.4 


28.3 


Silver 


Aff 


107 92 


107.66 


Sodium . 


Na 


23.05 


23.0 


Strontium 


Sr 


-. 87.6 


87.3 


Sulphur 


S 


32.06 


31.98 


Tantalum 


Ta 


182 6 


182. 


Tellurium 


Te 


125 


125. 


Terbium 


Tb 


160. 




Thallium 


Tl 


204 18 


203.7 


Thorium .... 


Th 


2326 


232.0 


Thulium ... 


Tu 


170.7 




Tin 


Sn 


119 


1188 


Titanium . . 


Ti 


48 


480 


Tungsten .... 


W 


184. 


183.6 


Uranium 


u 


239.6 


239.0 


Vanadium 


v 


51 4 


51 1 


Ytterbium 


Yb 


173 


172 6 


Yttrium 


Yt 


89 1 


88 9 


Zinc 


Zu 


65 3 


65 1 


Zirconium . . 


Zr 


90 6 


90.4 











It is evident that in many instances the values given in 
these two tables are based on different sets of data. 

If it be desired to learn the atomic mass of any element 
determined with reference to =16, on the basis of H = 1, 
it will only be necessary to fix on the ratio of to H, and 
then a simple calculation by proportion will yield the desired 
result. 

This ratio has been most carefully determined by several 
observers; following are some of the results obtained, 



ATOMS, ATOMIC MASS, VALENCE. 



H. O. 



Dumas 1 

Erdmann, Marchand 1 

Cooke, Richards (with Rayleigh's corrections) . 1 

Keiser 1 

Regnault, Rayleigh, Crafts 1 



15.96 

15.96 

15.869 

15.949 

15.91 

15.884 



Rayleigh 1 

Determination of Atomic Mass. The determination of the 
atomic masses of the elements is based on a chemical analysis 
of their compounds. 

It is, however, impossible to ascertain the atomic mass of 
an element solely from the results of an analysis of its com- 
pounds, for atoms cannot be isolated and then be weighed. 

If atoms of different elements were to combine with each 
other in only one proportion, a determination of the relative 
masses in which these elements are present in compounds, 
would permit of an inference as to the relative masses of the 
atoms. 

But elements frequently combine with each other in more 
than one proportion, and therefore, besides ascertaining the 
relative amounts by weight in which the different elements 
are present, it is absolutely necessary that the number of 
atoms constituting a molecule be known. 

Direct Determination. In order to determine the atomic 
mass of an element, the first step to be taken, is the analysis 
of all of the compounds of the element with hydrogen, assum- 
ing hydrogen to be adopted as the unit of atomic mass, and a 
comparison of the values found, in order to ascertain the 
smallest amount by weight of that element which exists in 
combination with hydrogen. 

A few problems will illustrate the method pursued. 

EXAMPLES. 

a. Required, the atomic mass of chlorine. 

The compound of chlorine with hydrogen is hydrochloric acid. This 
compound, subjected to most careful analysis, shows that in every 100 



58 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

parts by weight of hydrochloric, acid there are contained 2.74 parts by 
weight of hydrogen and 97.26 parts by weight of chlorine. 
Making the proportion: 

2.74: 97.26:: 1 : x, 
x = 35.5. 

This means that, in this compound, the amount of chlorine which 
combines with unit mass, i.e., with one atom of hydrogen, has a mass 
35.5 times as great as that of the hydrogen, and as no compound of 
hydrogen and chlorine is known which contains less of chlorine by 
weight than this amount, 35.5 is considered the smallest amount of this 
element which will enter into chemical combination with hydrogen. 

b. Required, the atomic mass of oxygen. 

Oxygen forms two compounds with hydrogen: water and hydrogen 
peroxide. 100 parts by weight of water consist of 11.112 parts of 
hydrogen and 88.888 parts of oxygen. 

11.112 : 88.888 ::!:*, 
x = 8.0. 

This means that, in this compound, 8 parts by weight of oxygen unite 
with 1 part by weight of hydrogen. 

100 parts of hydrogen peroxide consist of 5.882 parts of hydrogen and 
94.118 parts of oxygen. 

5.882 : 94.118 :: 1 : x, 
x = 16.0. 

This means that, in this compound, 16 parts by weight of oxygen unite 
with 1 part by weight of hydrogen, and as no other compounds of 
oxygen with hydrogen are known, besides these two here considered, 
i.e., water and hydrogen peroxide, it appears, that 8 parts by weight of 
oxygen, is the smallest amount of this element which enters into chemi- 
cal combination with 1 part by weight of hydrogen. 

The number which expresses the smallest weight of an 
element which will combine with or replace the unit weight 
of hydrogen, is called the chemical equivalent of that element. 
The atomic mass must be identical with, or must be a multiple 
of, this value. 



ATOMS, ATOMIC MASS, VALENCE. 59 

Indirect Determination. In cases where the element, the 
atomic mass of which is sought, does not form a compound 
with hydrogen, if that be the unit to which the atomic masses 
are referred, the atomic mass of the element is determined 
indirectly, that is, with reference to some other element, the 
atomic mass of which has been directly determined. The 
atomic masses of many, if not of most, of the elements have 
been determined in this manner. 

EXAMPLE : 100 parts of sodium chloride consist of 60.68 parts of 
chlorine aud 39.32 parts of sodium. 

As 35.5 parts of chlorine combine with 1 part of hydrogen, the amount 
of sodium which combines with 35.5 parts of chlorine represents the 
atomic mass of the sodium. 

60.68 : 39.32 :: 35.5 : x t 
x = 23. 

Therefore the atomic mass of sodium is 23, of course, on the supposi- 
tion that the molecule of sodium chloride consists of only one atom of 
chlorine and one atom of sodium. 

When the relative mass of an element in combination with 
one atom of hydrogen has been thus determined, directly or 
indirectly, there remain to be ascertained the number of hy- 
drogen atoms in the compound; the mass of the other con- 
stituent, combined with these hydrogen atoms, represents 
the total atomic mass of that element. 

Aids in Determining Atomic Mass: Vapor Density. When 
the compounds analyzed can be vaporized without decompo- 
sition, a determination of the vapor density affords the means 
of determining their molecular mass. The weights of equal 
volumes of gases bear to one another the same ratio as the 
atomic masses of those elements.* Thus, 

1 litre of hydrogen weighs 0.0896 gramme. 
1 " " nitrogen " 1.2544 grammes. 
1 " " oxygen " 1.4336 " 

* Excepting mercury, cadmium, zinc, phosphorus, and arsenic 



60 LECTURE-NOT KS OX THEORETICAL CHEMISTRY. 

The ratio of the atomic masses of these elements is practically 
the same as that shown by the figures, viz., 1 : 14 : 16. 

According to the hypothesis of Avogadro, "equal volumes 
of all gases, under the same conditions of temperature and 
pressure, contain the same number of molecules." As before 
stated, the weights of equal volumes of gases are readily 
determined; these weights bear the same relation to each 
other as do the masses of the molecules of these substances; 
hence it follows, that the molecular mass of all substances 
is directly proportional to the specific gravity of these 
substances in the state of a perfect gas. 

Under the standard conditions of temperature and pressure, 
one litre of hydrogen weighs 0.0896 gramme, and one litre of 
hydrochloric acid gas weighs 1.6352 grammes. The weight 

16352 

of a molecule of hydrochloric acid must therefore be * = 

o y o 

18.25 times as great as that of a molecule of hydrogen. 

18.25 parts by weight of hydrochloric acid gas consist of 
0.5 of hydrogen combined with 17.75 of chlorine. Therefore 
36.5, that is, 18.25 X 2, contains unit weight of hydrogen, 
and hence is the smallest number that can be adopted as the 
molecular mass of hydrochloric acid. 

As seen above, the molecule of hydrochloric acid is 18.25 
times as heavy as that of hydrogen; therefore, if the atom 
of hydrogen is 1, the molecular mass of hydrogen must be 
36.50 9 
18.25 : 

The atom of hydrogen is the unit of the atomic masses, and 
the molecule of hydrogen, consisting of two atoms, has been 
adopted as the standard for the specific gravity of gases. 
Hence, the molecular mass of any substance is equal to twice 
its specific gravity in the state of gas. 

To return to two of the examples previously given, those 
referring to hydrochloric acid and to water. 

As the molecular mass of every substance is the sum of its 



ATOMS, ATOMIC MASS, VALENCE. 61 

atomic masses, the values obtained by analysis the combin- 
ing masses must, when added together, result in either the 
molecular mass, or in a number of which the molecular mass 
is a multiple. 

Analysis has shown, that for every 1 part by weight of 
hydrogen in hydrochloric acid there are 35.5 parts by weight 
of chlorine. Hence 1 -f 35.5 = 36.5 is the molecular mass of 
hydrochloric acid, or if not, then the molecular mass of 
hydrochloric acid must be some multiple of this value. 

The vapor density of hydrochloric acid is found to be 
18.25. As the molecular mass of a substance is equal to 
twice its vapor density, 18.25 X 2 = 36.5 must be the molec- 
ular mass of hydrochloric acid, as previously stated. But 
this is also the value found by analysis; therefore hydrochloric 
acid must consist of one atom of hydrogen and one atom of 
chlorine, and the atomic mass of chlorine must therefore be 
36.5 - 1.0 = 35.5. 

Now, turning to the other example. Analysis of water 
shows that 1 part by weight of hydrogen combines with 8 
parts by weight of oxygen. 1 -j- 8 = 9 ; therefore 9 must be 
the molecular mass of water, or else the molecular mass of 
water must be some multiple of this value. 

The vapor density of water is = 9. The molecular mass 
of water is therefore equal to 9 X 2 = 18. 

The combining masses of hydrogen and of oxygen in water 
were, by analysis, found to be respectively 1 and 8. But the 
molecular mass was found to be twice this value, that is, 18. 
and therefore a molecule of water must contain twice as 
much of each constituent, that is to say, 2 of hydrogen and 
16 of oxygen, and the atomic mass of oxygen is therefore 16.* 

Atomic Heat. When the vapor density of an element 
cannot be obtained, then, in order to fix upon its atomic 
mass, recourse is often had to the fact discovered by Dulong 
and Petit in 1819, that the specific heat of an element is 
inversely proportional to its atomic mass. 

* Assuming the molecule of water to consist of three atoms. 



62 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

Specific heat is the ratio of the amount of heat required to 
raise a given weight of a body one degree in temperature, 
compared to the amount of heat required to raise the same 
weight of water to the same extent. 

The product of the specific heat by the atomic mass is 
approximately a constant; it is called the atomic heat. Its 
average value is 6.4, and the atomic mass of an element may 
therefore be approximately obtained by dividing the specific 
heat of the element, in the solid state, into 6. 4. 

EXAMPLE: 100 parts of chloride of silver consist of 75.26 parts of 
silver and 24.74 parts of chlorine. 

As 35.5 parts of chlorine combine with 1 part of hydrogen, the 
amount of silver which combines with 35.5 parts of chlorine must be 
the atomic mass of silver. 

24.74 : 75.26 :: 35.5 : as 

x = 108. 

Hence the atomic mass of Ag = 108. 

To confirm, or to dispose of, the assumption that this value represents 
the mass of one atom of Ag, the constant 6.4 is divided by the specific 
heat of silver. The specific heat of silver has been ascertained to be 
0.057. 

6.400 : 0.057 = 112. 

This value 112 is near enough to 108 to show that this represents the 
mass of one atom, and not of several atoms of silver 

To a limited extent the principle here referred to can also 
be extended to chemical compounds, for the specific heat of 
elements is practically the same when they are in a state of 
combination, as when they are in a free state. 

The molecular mass of a compound, multiplied by its 
specific heat, is equal to as many times 6.4 as there are atoms 
in the molecule. 

The specific heat of sodium chloride, for instance, is 0.214. 
Its molecular mass, on the assumption that it consists of one 



ATOMS, ATOMIC MASS, VALENCE. 63 

atom of sodium and one atom of chlorine, is 23.0 -f- 35.5 = 
58.5. 

58.5 X 0.214 = 12.52; 
12.52 -f- 6.4 = about 2, 

thus confirming the view above assumed in regard to the 
constitution of the molecule of sodium chloride. 

Isomorphism. This property was at one time regarded as a 
valuable aid in the determination of the atomic mass of ele- 
ments. 

Mitscherlich believed, that isomorphism, which he defined 
as identity of crystalline form, was due only to the number 
and the arrangement of the atoms in a molecule, and that 
it was entirely independent of the chemical nature of these 
atoms. He taught, that an equal number of atoms united 
in the same manner, gives the same crystalline form. 

This statement, if it were borne out by the facts, would 
furnish a valuable guide in atomic-mass determinations. For, 
two compounds being isoinorphous, it could be assumed that 
they contained the same number of atoms in their molecules. 
Then, knowing the atomic masses of the elements in the 
molecule of one of these substances, the atomic mass of one 
element in the other substance could be easily calculated. 

However, it can readily be shown that this method does not 
give reliable results, at least not, if the broad meaning assigned 
by Mitscherlich to the term isomorphism, be retained. 

Valence. It has been established by experiment that some 
elements will enter into chemical combination in but one 
proportion, while other elements will readily enter into com- 
bination in more than one proportion. 

To account for these facts, the hypothesis has been advanced, 
that this power of forming combinations is inherent in the 
atoms. 

This property is usually designated as the valence, the 
valency, atomicity, quantivalence, or the atomic value of the 



64 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 

atoms, and the valence of an element is generally expressed 
by the number of hydrogen atoms, or their chemical equiv- 
alent, which one atom of that element can combine with, or 
replace. Thus : 

1 atom of Cl combines with 1 atom of H. 
1 " " " 2 atoms of H. 

1 <e <e N <e ii 3 tf (e fe 

^ <( " Q " " 4 " " 

^ p (( K it <( <.t 

From this it is evident that oxygen can exhibit twice, nitrogen 
three, carbon four, and phosphorus five times, the combining 
power of the hydrogen atom. 

The relation between the chemical equivalent of an ele- 
ment and its atomic mass, is a simple one. 

The atomic mass, is either equal to, or it is two, three, four, 
five, six, seven, or eight times as great as the chemical 
equivalent. 

This relation is expressed by the formula: 

A = E X V, 

where A = atomic mass, 

E = chemical equivalent, 
V = valence. 

Standard of Valence. The combining power of an atom 
of hydrogen is usually selected as the unit of valence, 
and the combining values of the atoms of other elements 
are expressed in terms of this unit. 

When an element can combine with or replace hydrogen, 
atom for atom, it is termed a monad from the Greek yuoVo?, 
one; if an element combines with, or takes the place of, two 
atoms of hydrogen, it is termed a dyad; if three, a triad; if 
four, a tetrad; if five, a pentad; if six, a hexad, and so on. 

Elements having an odd number of bonds (monads, triads, 



ATOMS, ATOMIC MASS, VALENCE. 65 

pentads, heptads), are termed perissads; those having an even 
number of bonds (dyads, tetrads, hexads, octads), are termed 
artiads. 

Manner of Designating Valence. The valence of an ele- 
ment is represented by Roman numerals placed above, or by 
dashes, called bonds, which are placed at the side of the 
symbol of the element; the number of the dashes indicates 
the valence. Thus, 

H- 0- NE Ci Pi 
indicate that. 

H is a monad element, 
' dyad 
N " triad " 
" tetrad " 
P " pentad " 

Variable Valence. The position of these bonds is abso- 
lutely immaterial, their number only possesses significance. 

With but few exceptions the elements can exhibit varia- 
tions in their valence, and when this is done, the valence is 
generally varied by two bonds. 

Thus, a monad may be transfomed into a triad or a pentad, 
while a dyad can be caused to act as a tetrad or a hexad. 

In order to account for this, the assumption is made, that 
when a change in valence takes place, two bonds neutralize 
each other, as indicated in the figure on page 66. 

It certainly seems, that this idea of intra-linkage, that is to 
say, the union of some of the affinities of an atom with other 
affinities of the same atom, accounts well for the phenomenon 
of variable valence. 

Based on certain observations concerning the variable 
valence of nitrogen and of phosphorus, it has been assumed, 
that valence is a property of atoms dependent upon varying 
conditions chiefly upon the temperature. It has been held. 



66 



LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



that at low temperatures the valence of the elements is greater, 
while at higher temperatures the valence is decreased. How- 
ever, there seem to be serious objections to the acceptance of 
this view. 

Owing to the difficulty, not to say impossibility, of determin- 
ing the true cause of variable valence, Wurtz suggested, that 
the idea of a fixed valence of the atoms be abandoned, and 
that the valence exhibited by an atom in any given combina- 
tion be regarded as the outcome of the attractive forces of 




all of the atoms in that combination. He believed a knowl- 
edge of the valence which an element exhibits in any given 
compound to be of far greater importance, than all attempts 
could be, which might be made for the determination of a 
fixed valence. 

Remsen has proposed to designate the valence of an atom 
in the sense that Wurtz suggested, as the " apparent valence," 
and to reserve for valence regarded as a fixed property of the 
atom, the term "true valence." 

Determination of Valence. When elements replace one 
another in chemical combinations, the number of atoms of 
the elements taking part in the reaction, depends to a certain 
extent upon their respective valence. 



ATOMS, ATOMIC MASS, VALENCE. 67 

One atom of a monad element can of course be replaced 
only by one atom of some other monad element. One atom 
of a dyad can be replaced by one atom of some other dyad, or 
by two monad atoms; a triad may be replaced by three 
monad atoms, or by one dyad and one monad atom, or by 
some one other triad atom; a tetrad can be replaced by four 
monad atoms, by two dyad atoms, one triad and one monad, 
or by one atom of another tetrad element. 

The determination of the valence of the elements is there- 
fore an important matter. 

If the degree of combining power, the valence, which an 
atom of hydrogen possesses, be accepted as the unit, then the 
determination of the valence of those elements which form 
compounds with hydrogen, and of which the molecular mass 
can be determined, proves a simple matter. 

For instance, in order to determine the valence of oxygen, 
all compounds of oxygen with hydrogen must be analyzed. 

Two such compounds exist, and of these two, water has been 
found to contain the smallest proportion of oxygen to hydro- 
gen. It is therefore assumed, that in one molecule of water 
there is but one atom of oxygen. 

Analysis has shown that sixteen parts by weight of oxygen 
are combined with two parts by weight of hydrogen. The 
atomic mass of oxygen is 16. Therefore, as the smallest 
amount of oxygen known to exist in chemical combination, 
an atom of oxygen, is not known to occur in combination 
with less than two atoms of hydrogen, each of which possesses 
the valence one, the valence of an atom of oxygen must be 
two. 

Even if no compound of an element with hydrogen is 
known, the valence of the element referred to the atom of hy- 
drogen as standard, can be ascertained by the indirect method, 
by the aid of chlorine, bromine, etc., as previously explained 
in the determination of atomic masses; for this, a knowledge 
of the molecular mass of the compound is, however, essential. 



68 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

If elements exhibit variable valence, and, as already stated, 
nearly all of them do, it is desirable that there should be 
determined, what might be termed, their minimum and their 
maximum valence. 

By minimum valence is meant the lowest valence which an 
element is Known to exhibit in any combination; and by 
maximum valence, the highest combining power which it is 
known to possess. 

To ascertain these values, of course an analysis of all of the 
compounds of an element would be necessary. Few elements 
exhibit more than two powers of valence. 



CHEMICAL FORMULAE. 69 



CHAPTER V. 

CHEMICAL FORMULA. 

Introductory. A molecule may be defined as the smallest 
particle of matter which can exist uncombined, or, as the 
smallest quantity of matter in which its properties inhere. 

Molecules of the elements consist of atoms of the same kind 
of matter; molecules of compounds are combinations of atoms 
of different kinds of matter. 

Chemical analysis readily affords answer to the query 
whether a given substance consists of one or of more than 
one kind of matter, in other words, whether the molecules of 
a given substance are composed of atoms of the same, or of 
various kinds. 

Furthermore, chemical analysis permits of the determina- 
tion of the percentage composition of a compound substance, 
but when it comes to the assigning of a chemical formula 
a chemical formula being the expression in symbols of the 
chemical constitution of a body the domain of experimental 
research no longer affords adequate data, and the aid of 
theory must be invoked. 

Determination of Empirical Formulae. The simplest ex- 
pression of the ratio of the atoms in a molecule, is obtained by 
dividing the percentage amount of each element occurring in 
the molecule by its atomic mass, and then finding the simplest 
set of whole numbers which bear to one another the ratio of 
the quotients found. 

These figures represent the relative number of atoms of each 
constituent present. Thus, for instance, let it be required to 



70 LECTURE NOTES ON THEORETICAL CHEMISTRY. 

ascertain the formula of a substance having the following 
composition : 

Carbon 52.18 per cent. 

Hydrogen 13.04 " " 

Oxygen 34.78 " " 

The following calculation will yield the desired result : 
C. 52.18 -4- 12 = 4.35 = 2. -f 
H. 13.04 + 1 = 13.04 = 6. + 
0. 34.78 + 16 = 2.17 = 1. + 

This shows that the elements carbon, hydrogen, and oxygen 
are present in the proportion of 2 : 6 : 1, and therefore the 
simplest formula of this substance would be C 2 H 6 0. 

The ratio in which the atoms forming a compound are 
present, can be readily determined if the percentage composi- 
tion of the compound and the specific heat of one of the com- 
ponents be known. 

EXAMPLE : Analysis of an oxide of iron showed it to consist of 30 
per cent of oxygen and 70 per cent of iron. 

Atomic mass of oxygen = 16. 
Specific heat of iron = 0.114. 

6.4 -H 0.114 = 56. -f 
Hence 56. is approximately the atomic mass of the iron. 

Assuming that there is present in the molecule at least one atom of 
Fe, and of course there can be no less, then: 
70 : 30 : : 56 : 16*. 

* = 1.5. 

This means that for every atom of iron in the molecule there are 
present H atoms of oxygen. But as half-atoms cannot exist, the atoms 
of Fe and the O are present in the proportion of 2 : 3. 

Of course this proceeding gives only approximately correct 
results, as allowance must always be made for experimental 
errors and inaccuracies. 

The formula expressing simply the ratio in which the 
elements forming a compound, are present, is termed the 
empirical formula of the substance. Such a formula, although 



CHEMICAL FORMULJE. 71 

exhibiting the ratio in which the different elements forming 
a substance are present, leaves its actual constitution un- 
determined. 

Determination of Molecular Formulae. A molecular formula 
is intended to indicate the number of atoms of each of the 
elements in a molecule, as well as to show the mere numerical 
ratio obtaining between them. The molecular formula of a 
substance may therefore be identical with, or a multiple of, the 
empirical formula of that substance. 

In order to determine the correct molecular formula of a 
body, the molecular mass of the substance must be known, 
when a simple calculation will yield the desired result. 

Thus, for instance, if the percentage composition of a 
substance be given as : 

Carbon 52.18 

Hydrogen 13.04 

Oxygen 34.78 

and the molecular mass as 46, then the molecular formula 
would be calculated as follows: 

C. 100 : 52.18 : : 46 : x = 24, total atomic mass of the carbon. 
H. 100 : 13.04:: 46 :-x = 6, " " " "hydrogen. 
0. 100:34.78: : 46:2: = 16, ' " " " "oxygen. 

As the atomic masses of carbon, hydrogen, and oxygen are 
respectively 12, 1, and 16, 

94 

2, the number of atoms of C in 1 molecule. 

1/& 

f* 

* __ c (( <( tf u TJ tt tc 

~\ f\ 

P -i <- u u <( (( f) t( tt 

16 ~ 

and the molecular formula of this substance is, therefore, 
C.H.O. 



72 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

There are several methods of determining the molecular 
mass of substances. 

Determination of Molecular Mass: Method of Chemical 
Analysis. This method can be resorted to in all cases. It 
involves a study of the chemical behavior of the body under 
consideration, an analysis of its compounds and derivatives, 
and the drawing of certain conclusions from the results thus 
obtained. 

This method of procedure can best be illustrated by an 
example. Suppose it were required to determine the molecu- 
lar mass of nitric acid. Analysis of numerous salts of this 
acid show it to be monobasic, that is to say, show that it con- 
tains but one atom of hydrogen which is replaceable by metals. 

This having been ascertained, careful analysis is made of 
the nitric acid salt of some metal, the atomic mass of which 
has been accurately established. Nitrate of silver answers this 
purpose well. This compound contains 63.53 per cent of 
silver. 

Making the proportion : 

100 : 63.53 : : x : 108, 

x - 170. 

That is, the molecular mass of nitrate of silver is 170. But 
this compound differs from nitric acid in having one atom of 
silver in the place of one atom of hydrogen; 
therefore, 170 
minus 108, the atomic mass of silver, 

is 62, and this 

plus 1, the atomic mass of hydrogen, 

equals 63, the molecular mass of nitric acid, the 
value sought. 

Method of Vapor-Density Determination. This method is 
applicable only to those substances which can be trans- 
formed into the gaseous condition without suffering decom- 
position. 



CHEMICAL FORMULAE. 73 

As stated in the previous chapter, equal volumes of all 
gases and vapors, under the same conditions of temperature 
and pressure, contain an equal number of molecules. 

The specific gravity of gases and vapors is referred to 
H. = 1.0; molecular weights are referred to H 2 = 2.0. The 
molecular mass of a substance is therefore obtained by multi- 
plying the specific gravity of its vapor referred to hydrogen, 
by 2. 

In case that the specific gravity of a substance in the 
gaseous condition has been referred to air = 1.0, then its 
molecular mass is ascertained by multiplying this specific 
gravity value by 2 X 14.43, that is, by 28.86, for the specific 
gravity of air referred to hydrogen is 14.43. 

The different methods used in making determinations of 
the vapor density of a substance have previously been fully 
discussed, and may be referred to again in this connection.* 

Methods based on Properties of Substances when in Solu- 
tion. The principal methods which call for consideration 
under this heading rest, respectively, on the determination of 
the osmotic pressure, on the lowering of the vapor-pressure, 
on the rise of the boiling-point, and on the depression of the 
freezing-point of solutions. 

METHOD A. Osmotic Pressure. Substances when brought 
into a state of dilute solution exhibit in their behavior a 
marked resemblance to their deportment when in the gaseous 
condition. 

Experience has taught, that the particles of a substance 
when in dilute solution exercise a pressure, called the osmotic 
pressure, which is equal to the pressure that would be exerted 
by the same amount of the substance if the solvent were re- 
moved, and the substance, transformed into a gas, were, at the 
same temperature, made to occupy the same volume previously 
filled by the solution. 

* Chapter II. 



74 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

This fact, as formulated by Van 't Hoff , is thus stated : The 
osmotic pressure in a solution, like the tension of a gjis, is in- 
dependent of the nature of the molecules, but is directly pro- 
portional to their number, and is equal to the corresponding 
tension exercised by the body in the gaseous state. 

The osmotic pressure method, therefore, affords a means of 
indirectly determining vapor-densities, and from these, of 
course, the molecular masses can readily be calculated by aid 
of AvogadiVs law. 

The experimental difficulties of making direct determina- 
tions of osmotic pressure are very great, and such determina- 
tions are therefore but rarely made. There are, however, 
several serviceable methods which permit of an indirect 
determination of the osmotic pressure, and as the lowering of 
the vapor-tension and the lowering of the freezing-point of 
solutions are proportional to their osmotic pressure, measure- 
ments of this character are made use of for the determination 
of molecular mass. 

METHOD B. Lowering of the Vapor-pressure. The vapor- 
pressure of a solvent is lowered by the addition of a non- 
volatile substance. This lowering of the vapor pressure is 
proportional to the quantity of the substance dissolved, and is 
equal to the number of the molecules dissolved, divided by the 
number of molecules of the solvent. 

Basing on this fact, the molecular mass of a substance can 
be ascertained, after securing the experimental data necessary, 
by the formula : 



where, M = molecular mass of the substance dissolved ; 

M Q = " " " solvent ascertained by a 

vapor-density determination; 

p vapor-pressure of the pure solvent at any given 
temperature ; 



CHEMICAL FORMULAE. 75 

p' = vapor-pressure of a solution in which for each 100 
grammes of solvent, there are m grammes of dis- 
solved substance. 

But as the experimental difficulties to be overcome in this 
method are also very great, its application also is but limited. 

METHOD C. Elevation of the Boiling-point. This method, 
due to Beckmann, is comparatively simple and furnishes re- 
liable results. Originally it was intended to be used only in 
determinations where the dissolved substance was n on- volatile, 
but it has lately been so extended by Xernst that it can now 
also be applied in the case of volatile substances. 

Determinations by this method are made in a glass flask 
provided with a condenser and furnished with a thermometer 
very accurately graduated. The supply of heat is care- 
fully regulated, and is generally transmitted to the liquid by 
means of a platinum wire fused into the apparatus. 

When the temperature of the boiling solution has become 
constant, a weighed quantity of the substance to be dissolved 
is introduced, and the elevation of the boiling-point caused 
thereby, is noted. 

Calculation of the molecular mass is effected by the formula: 



where M = molecular mass of the dissolved substance; 
m = as in the previous method ; 
t = observed elevation of boiling-point; 
E = molecular elevation of boiling-point, calculated 
from the heat of vaporization of 1 gramme of 
the solvent and its boiling-point, in absolute 
degrees of temperature. 

METHOD D. Depression of the Freezing-point. The freez- 
ing-point of solvents is lowered when substances are dissolved 
in them, and this lowering of the freezing-point takes place 
according to a law which Raoult first believed could be stated: 



76 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

The molecular mass of any substance, on dissolving in 100 
times the molecular mass of any solvent, lowers the freezing- 
point of the solvent by very nearly 0.63 C. 

Later investigations, however, have shown that this state- 
ment is not universally true, and this formulation of the law 
had therefore to be abandoned. 

Let: 

A = the coefficient of lowering of the temperature of solidification, 
that is, the depression of the freezing-point produced by 
the solution of 1.0 gramme of substance in 100.0 grammes 
of the solvent ; 

T = the molecular coefficient of lowering, that is, the depression 
of the freezing-point produced by the solution of one 
gramme-molecule (the molecular mass in grammes), of the 
substance, in 100 grammes of the solvent ; 
M = the molecular mass of the dissolved substance. 
Then, 

T=MA, 

and, 

M=- 

~ A 

The value of T is ascertained for each solvent, by direct 
experiment by determining the depression of the freezing- 
point which is produced by substances, the molecular mass of 
which is known. 

The value of A is found by determining the freezing-point 
of the solvent, first without, and then after introduction of 
the substance to be dissolved. 

Then, if: 

P = weight of the solvent ; 
P' = weight of the dissolved substance ; 

JT=the lowering of the freezing-point produced in the experi- 
ment; 

P_ 

p^xHiob' 



CHEMICAL FORMULA. W 

The mean value of T, as determined by numerous experi- 
periments, is, for: 

Acetic acid = 38.6; 
Formic acid = 28.0; 
Benzene = 49.0; 

Nitrobenzene = 70.5; 

( 18.5 (for organic substances, some salts 
of dyad metals, all the feeble bases 
Water =J and acids); 

37.0 (for alkaline and alkaline earthy 
salts, and for all the strong acids 
and bases). 

The following problem will show the manner of effecting 
molecular mass determinations by the Raoult method. 

EXAMPLE : Determine the molecular mass of propionic acid. 

The freezing-point of a sample of acetic acid was found to be 16.490 C. 
Taking 62.014 grammes of this acid and adding to it 0.2540 gramme of 
pure propionic acid, the solidifying point of the mixture was found to 
be 16.277 C. The value of Tfor acetic acid = 38.6. 

The lowering of the freezing-point is : 

16.490 C. 
less 16.277 C. 



As: 



K= 0.213 C. 
P 62.014 grammes. 
P = 0.254 



= 0.213 62 - 14 



0.254X100 
A = 0.5199, 

and as the molecular mass of the dissolved substance is calculated by 
the formula : 



in this instance : 



while the calculated molecular mass of propionic acid, C 2 H 5 COOH, is 74. 



78 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 



CHAPTER VI. 
THE STRUCTURE OF MOLECULES. 

Introductory. In order to gain an idea of the manner in 
which the atoms are grouped to form a molecule of any sub- 
stance, this substance must be submitted to an exhaustive 
examination. 

If feasible, physical as well as chemical methods must be 
employed, with a view to gleaning all information possible, 
regarding the behavior of this substance under the most 
varied conditions. 

Let it be required, for instance, to study a compound of 
carbon, hydrogen, and oxygen, with the purpose of gaining 
an insight into its structural condition, in order that a proper 
formula may be assigned to it. 

The information first sought for in such a problem would 
probably be concerning the behavior of the atoms of the 
different constituents : whether, for instance, all the atoms of 
an element behave alike, or whether a difference in their 
behavior could be determined. In the case of hydrogen, the. 
question would be, whether its atoms may all be replaced by a 
metal, or all by a non-metal, or whether they are replaceable 
in part by the one and in part by the other. 

As regards the oxygen atoms, attempts would be made to 
ascertain (b}^ making substitution-products), whether some of 
these atoms, and if so, what number, are united respectively to 
the carbon and to the hydrogen atoms; this would permit 
an inference as to how many groups of hydroxyl (OH) and 
of carbonyl (CO) exist in the molecule. 

Endeavors would be made to prepare the compound in 
question by synthesis, with a view to gaining further 



THE STRUCTURE OF MOLECULES. 79 

information concerning the grouping of the component 
elements. Finally, the valence of the elements forming the 
compound would be carefully considered, so that, in the light 
of the knowledge obtained with regard to their grouping, a 
formula might be devised in which due regard would be paid 
to the valence of the different constituents. 

In studying the physical properties of solids and liquids 
with a view of ascertaining the structure of their molecules, 
due attention must be given to the subjects of molecular 
volumes and molecular refraction, as well as to the action 
which such substances may exercise on polarized light. 

Molecular Volume. This term is applied to the quotient 
obtained by dividing the molecular mass of a substance by 
its specific gravity, when in the liquid state and at the boil- 
ing point of the liquid, under a pressure of 760 mm. 

The determination of the molecular volume is a matter of 
importance chiefly with organic compounds. 

An intimate relation exists between the constitution of 
substances and their molecular volumes. 

Thus, in the following series of organic acids, 

Formic, H.COOH, 

Acetic, CH 3 .COOH, 

Propionic, C 2 H 5 .COOH, 

Butyric, C 3 H 7 .COOH, 

each member differs from the preceding member of the 
series by CH . If the molecular volumes of these acids be 
calculated, it will be found that the molecular volume of 
each member of this series differs from the preceding member 
of the series by the constant 22. The conclusion therefore 
seems justified, that the molecular volume of CH 2 is equal 
to 22. 

From a great number of observations, Kopp, the pioneer 
in this field of research, deduced a series of values for the 



80 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 

specific volumes of the elements when in combination, and in 
certain classes of compounds. 

C = 11.0. 

H = 5.5. 

12.2 when united to one element by both bonds. 

= 7.8 " " " " " " one bond. 

S = 28.6 " " " " " " both bonds. 
S = 22.6 " " " " " " one bond. 
Cl = 22.8. 
Br = 27.8. 

1 = 37.5. 

N = 2.3 (in compounds of the ammonia type). 

A knowledge of these data will often permit an inference 
as to the probable grouping of certain elements in a molecule. 

Thus, the molecular volume of acetone, at its boiling-point, 
is found to be 77.5. Calculating the molecular volume of 
acetone by aid of the figures just given, 

C - 3 X 11 = 33.0 
H = 6 X 5.5 = 33.0 
= 1 X 12.2 = 12.2 



the result would be 78.2, assuming that in this substance 
the oxygen atom is united by both bonds to one element. 

If the oxygen atom were united to one element by but one 
bond, the result would be different, namely : 

C = 3 X 11 = 33.0 
H = 6 X 5.5 = 33.0 

= 1 x 7.8 = 7.8 

73.8 



THE STRUCTURE OF MOLECULES. 81 

X 

The former figure evidently agrees far more closely with the 
observed value than the latter, and the constitution of the 
acetone molecule is therefore assumed to be indicated by the 
following structural formula: 



C'H, 

C = 0. 



in. 



Attempts to draw conclusions with regard to the mo- 
lecular structure of solid substances, from their molecular 
volumes, has shown that isomorphous compounds, that is to 
say, compounds which have an analogous composition and 
which crystallize in the same form, have molecular volumes 
which are equal or nearly equal. 

Thus, the molecular volumes of the sulphates of calcium, 
barium, and strontium, which constitute an isomorphous 
group, range from 45.3 to 51.4, and the sulphates of magne- 
sium, zinc, nickel, cobalt, and iron, each crystallized with 
seven molecules of water, all have their molecular volumes 
ranging between 145.5 and 147.5. 

Molecular Refraction. When a ray of light passes from 
one medium into another which is more dense, the ray is 
bent out of its course and is deflected towards a line con- 
ceived at right angles, i.e., perpendicular, to the surface of the 
more dense medium. 

If a circle be drawn from A as centre, with a radius equal to 
unity, and if from the points m and JP, where the circle cuts the 
incident and the refracted ray, the lines inn and pq be drawn 
perpendicular to BC, mn is called the sine of the angle of 
incidence, LAB, and ^9 the sine of the angle of refraction. 
KAC. 



82 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 




The ratio between the sines of the angle of incidence and 
of refraction, is termed the index of refraction. 

It has been found that an intimate relation exists be- 
tween the refracting power of certain substances and their 
constitution. 

The specific refractive power of a substance is expressed by 
the formula: 

nl 



where n is the index of refraction, and d is the specific 
gravity of the substance. 

This expression does not hold strictly good for the same 
substance when in different states of aggregation; thus, for 
water in the liquid state, the specific refractive power, cal- 
culated by above formula, is equal to 0.3338, while for steam, 
it is equal to 0.3101. 

A formula advanced at about the same time, but inde- 
pendently, by Lorenz of Copenhagen and by Lorentz in 



THE STfcUCTtJRE OF MOLECULES. 83 

Leyden, in the year 1880, yields results much more satis- 
factory in this respect. 

This formula, expressing the refraction-equivalent, is : 

n* - 1 I 



and gives, for instance, for liquid water the value 0.2061, for 
steam, 0.2068, values that are almost identical. 

If the molecular mass of a substance is multiplied by its 
refraction-equivalent, thus: 

n* -I 1 
< w f + 2'<7' 

the resulting product is termed the molecular refraction- 
equivalent of the substance, and represents the specific 
refracting power of the molecule. 

In general, this specific refracting power of the molecule 
has been found to be equal to the sum of the refractive 
powers of the atoms of which the molecule consists. 

The refraction-equivalent of several kinds of atoms has 
been carefully determined, notably by Bruhl and by Landolt, 
by the comparing of two compounds which differed from one 
another by only one or two atoms of the element investigated. 
These researches have been conducted principally on organic 
substances, and several interesting and important relations 
have been traced. 

Thus, Bruhl found, that all substances in which the 
presence of doubly-linked carbon atoms was assumed, always 
possessed a molecular refractive power actually greater than 
was indicated by calculation from the refractive powers of 
the atoms, a fact which has proved of value in determining 
the molecular structure of some compounds. 

Thus, for instance, the molecular refraction of benzol is 
calculated to be : 



84 LECTlTRE-XOTES OK THEORETICAL CHEMISTRY. 

Carbon (single linkage) 2.365 x 6 = 14.190 

Hydrogen 1.103 X 6 = 6.618 

Double linking of carbon 1.836 X 3 5.508 

Calculated molecular refraction = 26.316 

Actual observation of n and d leads to the molecular refrac- 
tion value 25.93; this shows a fairly close agreement, and 
confirms the customary structural formula assigned to this 
substance. 

Magnetic Rotation of the Plane of Polarized Light. In 
1846 it was discovered by Faraday, that transparent sub- 
stances, when they are surrounded by a wire through which 
an electric current flows, or when they are placed in a 
magnetic field, become capable of rotating the plane of 
polarized light. 

Since 1882 W. H. Perkins has undertaken to investigate 
the relations existing between the amount of rotation pro- 
duced and the chemical constitution of the substances pro- 
ducing such rotation. Through his researches it has been 
learned, that the extent to which rotation is effected, depends 
upon the nature of the substance, upon the thickness of the 
section traversed by the light, upon the temperature, and upon 
the intensity of the magnetic field. Homologous series ex- 
hibit an additive character in this property; thus, for instance, 
it has been found that every CH 2 group produces an increase 
of 1.023 units. 

This power of rotating the plane of polarized light is of 
some value in determining the class of compounds to which a 
body belongs. Kelations are here found to exist, similar to 
those, that were noticed in discussing the bearing which the 
constitution of substances exercises on their molecular refrac- 
tion power. 

Isomerism. When two compounds have the same percen- 
tage composition and identical molecular masses, but exhibit 
different properties, the compounds are said to be isomeric. 



THE STRUCTURE OF MOLECULES. 85 

When their percentage composition is the same, but when 
the molecular mass of the one is a simple multiple of the 
molecular mass of the other, the compounds are said to be 
polymeric. 

The difference in the behavior of isomeric bodies may be 
exhibited in their chemical, their physical, and their optical 
properties. 

Such differences of properties were already at an early date 
assumed to be owing to. some variation in the arrangement, 
the grouping, of the atoms constituting the molecules; how- 
ever all atoms were conceived of as lying in one plane. The 
study of isomerism dates back to 1824, from which time, until 
1873, this view with regard to the nature of isomerism was 
held. 

Stereochemistry. AVislicenus in the year last named, after 
an exhaustive study of the grouping of the carbon, hydrogen, 
and oxygen atoms existent in lactic and in sarcolactic acids, 
announced the structural identity of these bodies, and stated 
that the difference between isorneric molecules which have the 
same structural formula, can only be explained by assuming 
that such molecules differ from one another by the arrange- 
ment, the grouping, of their atoms in space. 

If two atoms of hydrogen in CH 4 are replaced by two other 
monad atoms, for instance by chlorine, then, if the atoms are 
conceived as grouped in one plane, two isomers are possible, 
as shown by the following figure: 

Cl Cl 

I I 

Cl C H H C H 

I I 

H Cl 

In the one case, the chlorine atoms adjoin one another, in 
the other they do not. 

However, as a matter of fact, only one form of methylene 
chloride, CH 2 C1,, is known to exist, and if this view is to be 



86 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

expressed, the atoms must be regarded as grouped in such a 
manner, that the possibility of isomerism is excluded. 

A grouping of this kind is possible only, when the atoms 
forming the molecule are conceived of as grouped in space, 
and a form of structure which would meet the requirements 
is that of a tetrahedron, in which all of the other atoms 
would hold the same relation to the carbon atom, that the 
corners of a tetrahedron bear to the centre of the same; then 
the chlorine atoms, however one may conceive of their being 
placed, will always adjoin one another. 

The theory of the grouping of atoms in space, foreshad- 
owed by Wislicenus, was first distinctly advanced by Van't 
Hoff in September, 1874, and, independently, by Le Bel, a 
few months later in the same year. 

While the property previously alluded to, of rotating polar- 
ized light under the influence of magnetism, is quite general, 
certain substances exist, in which the power of rotating light 
is inherent, and which do not require the influence of elec- 
tricity to bring it into play. This has been known for some 
time; that certain crystalline solids are capable of thus natu- 
rally rotating polarized light, was first noticed in the mineral 
quartz, by Arago in 1811. 

Concerning this power in as far as certain crystalline solids 
possess it, it is believed to be owing to a definite spiral ar- 
rangement of their ultimate particles. At least this assump- 
tion is made very plausible by the crystallographic properties 
of such bodies; in fact an optically active body can be arti- 
ficially constructed, as first shown by Reusch in 18G9, by 
placing a number of mica plates on one another in such a 
manner that the optical axis of each plate is placed at a certain 
angle to the optical axis of the plate which it adjoins. 

The fact that certain substances in solution will rotate 
polarized light, was first noticed in sugar solutions by Biot, 
in 1815. This property of rotating polarized light when in a 
state of solution, is possessed by quite a number of substances; 



THE STRUCTURE OF MOLECULES. 



87 



these substances are all carbon compounds, and it was with 
the intention of affording an explanation of these phenomena, 
that Van't Hoff first advanced his theory. 

He assumed that the four valences of the carbon atoms of 
all such optically active substances are grouped about the car- 
bon atoms in space, and that each one of these valences is 
united to some atom or radical, all of the four atoms or 
radicals being unlike in kind. A carbon atom answering this 
requirement he denoted as asymmetric. 

Van't Hoff's theory affords a plausible explanation of the 
reason why two isomeric bodies may differ in their optical 
behavior. 

Let 1, 2, 3, 4 denote four different atoms or radicals united 
to a carbon atom, and let it be assumed that the resulting 
molecule is represented by the figure of a tetrahedron. Then 
it will be evident, from the accompanying sketch, that these 





different atoms or radicals can be grouped about the carbon 
atoms in such a manner, that the resulting figures, although 
presenting much similarity, are yet distinctively different and 
will not admit of superposition. 

If now one of these structures possesses the property of 
rotating a plane of polarized light from left to right, the 
other structure will rotate it from right to left, for inspection 
of the above sketch will show, that, in order to pursue the 
course 1, 2, 4 in figure A, one must travel in a direction 
opposite to the direction in which the hands of a clock move, 



88 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

while in figure B the course 1, 2, 4 is traced by moving in 
the direction followed by the hands of a clock. 

Van't Hoff advanced various proofs in support of his the- 
ory, and his claims have been most amply confirmed by 
others. Moreover, it is now regarded as probable that the 
converse of Van't Hoff's theory is also true, namely, that 
every asymmetric carbon group is optically active. This, 
however, must not induce the belief that every substance 
which contains asymmetric carbon atoms is optically active, 
for it seems most likely that every compound with asymmet- 
ric carbon atoms should exist in two forms, which rotate the 
plane of polarization to the same degree, but in an opposite 
sense, and that compounds are possible in which both modi- 
fications exist to an equal extent, and which therefore are 
optically inactive. 

Le Bel, who in November, 1874, followed Van't Hoff's 
announcement with an article bearing on the same subject, 
was led to his investigations and ultimately to the promulga- 
tion of his theory, also by the desire to explain certain optical 
phenomena displayed by some substances when in solution. 

Biot in 1819 and Gernez in 1864 had shown that sub- 
stances which are optically active when in solution, retain 
this property when in the vapor form; it therefore seemed 
probable that this property of affecting polarized light might 
be a property dependent upon the internal structure of the 
molecules, and not upon any peculiar arrangement of the 
molecules themselves. Working upon this supposition Le Bel 
was led to advance independently the idea that the atoms of 
such compounds must have a grouping in space, and he was 
thus brought to share with Van't Hoff the honor of founding 
the now famous doctrine of stereochemistry. 



CHEMICAL EQUATIONS AND CALCULATIONS. 89 



CHAPTER VII. 
CHEMICAL EQUATIONS AND CALCULATIONS. 

Definitions. A chemical symbol is the abbreviated designa- 
tion of an element which represents not only the name of the 
element, but also the definite proportion by weight in which 
the element will enter into chemical combination. 

Thus, the symbol of chlorine is Cl: the atomic mass of 
chlorine is 35.5, and this symbol Cl is not only an abbreviated 
expression of the name of the element, but is to suggest as well 
the atomic mass of that element, namely, 35.5. 

A chemical for mitl a is the expression in symbols of the 
chemical constitution of a compound. 

An empirical formula is the simplest expression of the ratio 
in which the elements composing the substance are present; 
e.g., empirical formula of acetic acid, CH 2 0. 

A molecular formula shows the absolute number of atoms 
of each of the elements combining to form the molecule, as 
well as the mere numerical ratio between them; e.g., molecu- 
lar formula of acetic acid, C 2 H 4 Q . 

A constitutional formula aims at illustrating the probable 
arrangement, the grouping, of the atoms in a molecule. 

The molecular formula may, and often does, coincide with 
the empirical formula; if not, it must be some simple multiple 
of the latter. 

A formula conveys three distinct ideas. It illustrates: 

A qualitative relation. 

A quantitative relation by weight. 

A quantitative relation by gaseous volume. 

Thus, the formula XH 3 shows : 



90 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

First, that NH 3 is a compound of nitrogen and hydrogen. 

Secondly, that NH 3 consists of fourteen parts by weight of 
nitrogen and three parts by weight of hydrogen. 

Thirdly, that one volume of nitrogen gas combines with 
three volumes of hydrogen gas to form two volumes of ammo- 
nia gas. 

A chemical equation is the expression in symbols or formulae 
of the changes that elements or compounds undergo when 
subjected to chemical or, in some instances, to physical influ- 
ences. As matter is indestructible, these expressions of change 
must of necessity be equations, for, whatever the change, noth- 
ing is lost. 

Three kinds of chemical equations may be distinguished: 
synthetical, analytical, and metathetical. 

Synthetical equations are those representing the union of 
elements or of compounds. 

EXAMPLE : 211 -f O = H 2 O. 

2KCl + PtCl 4 = K a PtCl.. 

Analytical equations illustrate the separation of a compound 
into its constituents. 

EXAMPLE : CuCO 3 -f heat = CaO -f CO 2 . 

Metathetical equations demonstrate the interchange of ele- 
ments or of radicals and the formation of new products. 
EXAMPLE : BaCl 2 + H 2 SO 4 = BaSO 4 + 2HC1. 
Some chemists, in the belief of obtaining thereby a more 
graphic representation of the reactions, prefer the writing of 
chemical equations in such a manner that the formulae of the 
factors taking part are placed in horizontal lines, they being 
so arranged, that the formulae of the resulting products appear 
placed in vertical columns. 

Thus, the reaction last given, could be written: 
Ba 01. 

S0 4 H, 

BaS0 4 -f 2HCJ1 
Metathetical equations or, as they are also called, equations 



CHEMICAL EQUATIONS AND CALCULATIONS. 



91 



of interchange claim attention most frequently, and, in this 
class, equations of oxidation and reduction present the most 
interesting problems.* 

Oxidizing Agents. Among the numerous oxidizing agents 
perhaps the most important are : 



Mode of Action. 



Ordinary Oxygen, 0, 
Ozone, 3 . 
Cl. Br. I. 



HN0 3 . 
HNO, 
HC10,. 

HC10. 
H 2 S0 4 cone. 

H 2 Mn 2 O e and corre- 
sponding salts. 



By direct union with a compound. 
By direct union with a compound. 
By direct union with a compound, 



or by combining with the hydrogen 

of water and liberating oxygen, 
2C1 + H 2 = 2HC1 + 0. 
2HNO, = H 2 + 2NO + O s . Some- 

times = H~ 2 + 2N -f 50. 
2HNO, = H 2 + 2X0 + 0. Some- 

times = H 2 + 2N + 30. 
2HC10, = 2HC1 + 30 2 . Or, HC1 .and 

various oxides of chlorine. 
2HC10 = 2HC1 + 0.. 
H 2 S0 4 + heat = HJSO, + = H 2 S 

+ 20, 
In acid solution: 

H 2 Mn 2 8 = H 2 
In alkaline solution : 
H,Mn a O. - H 2 
In neutral solution : 



2MnO -f 5 . 



Mn,0, 



4 . 



H.CrO.. 



or, 

H 2 Mn 2 8 = H 2 + 2MnO t + 3 . 
2H 2 Cr0 4 = 2H 2 + Cr 2 3 + 3 . 

Besides these, most of the higher metallic oxides and 

* Equations of oxidation and reduction are, however, not always 
motalhetical equations. 



92 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

their compounds can readily act as oxidizing agents. Thus, 
for instance, 

Pb0 2 = I'bO -f 0, 
MnO, = MnO + 0, 
Mn0 = 2MnO 0. 



Reducing Agents. The chief reducing agents are nascent 
hydrogen and, as a rule, those compounds of metals which 
possess a lower quantivalence than the metals can readily 
assume. Thus, for instance, 

SnO + = Sn0 2 , 
2FeO + = Fe 3 8 . 

Some of the acids readily act as reducing agents, as 
illustrated by the following: 

H 3 P0 2 + 2 = H 3 P0 4 , 
H 2 S0 3 + = H 2 S0 4 , 
H 3 C a 4 + 0==H,0 + 3CO a , 

H 2 S + = H 2 -f- S. 

And some hydrides of metals can also exercise this function : 

AsH a + 3 = H 3 As0 3 , 
PH 3 + 3 = H 3 P0 3 . 

Laws of Chemical Interchange. The laws governing 
chemical interchange have not yet been fully determined, but 
it has been found that two conditions exert an important 
bearing on the result. 

1st. Whenever a substance can be formed which is 
insoluble in the menstrnum present, this substance separates 
as a precipitate. 

2d. Whenever a gas can be formed, or any substance which 
is volatile at the temperature at which the experiment is 
made, this volatile product is set free. 

The law of interchange may also in general terms be stated 






CHEMICAL EQUATIONS AND CALCULATIONS. 93 

to be, the tendency to form those substances the formation of 
which develops the highest thermal effects. 

Interchange is always effected on terms regulated by the 
valence of the elements or radicals involved. That is to 
say, a monad element or radical can replace another monad 
element or radical, atom by atom; a dyad element or radical 
can replace another dyad element or radical atom by atom, 
while, to effect a similar exchange with monad elements, two 
atoms of a monad element or radical are needed. 

Writing of Chemical Equations : Analytical Method. Bear- 
ing in mind the statements made, to write an equation of in- 
terchange, the following simple suggestions may be followed : 

1st. Place down as first member of the equation the sym- 
bols or formulae of the substances entering into the reaction, 
and place the plus sign between them. 

2d. Write as terms of the second member of the equation 
the symbols or formulae of the products resulting from the 
reaction. 

3d. Adjust the factors of the symbols or formulae so, that 
the interchange will result in an equation. 

The first step, as given above, needs no comment. 

The data for the second step must primarily be determined 
by actual experiment. In a great many cases, remembering 
the conditions that affect an interchange and which have 
been previously stated, there may be predicted, by means of 
equations, what products will be formed in a chemical 
metathesis; but it should also be remembered that a chemical 
equation differs in various ways from an algebraic equation : a 
chemical equation cannot be accepted as positively true unless 
verified by experiment; equal amounts cannot be subtracted 
from either side of a chemical equation, and leave it true, etc. 

The third step the adjusting of the factors is the im- 
portant one; and in order the better to illustrate the prin- 
ciples involved, it will be well to work out a few problems in 
this connection. 



94 LECTURE-NOTES OK" THEORETICAL CHEMISTRY. 

EXAMPLE A : Write an equation illustrating thut ferrous sulphate 
is oxidized to ferric sulphate by manganese dioxide, in the presence of 
sulphuric acid. 

In compliance with the directions just given : 

FeSO 4 + Mn0 2 + H 8 SO 4 = Fe 3 (SO 4 ) 3 -f MnSO 4 -f H 2 O. 

Oxidation signifies an increase in the combining power (the valence) 
of an element ; reduction signifies a decrease in the combining power. 
Hence an oxidizing agent, in exerting its influence, loses in valence; the 
substance oxidized experiences a corresponding increase in its valence. 

In this instance, 

2FeO + O = Fe 2 O 3 , 
MnO a =MnO-fO; 

hence the factor for FeSO 4 in the above equation is 2, and the factor 
forMnOa is 1. 

The presence of free sulphuric acid is indicated by the conditions of 
the problem. 

Therefore, the desired equation will be : 

2FeS0 4 -f MnO, -f 2H 2 SO 4 = Fe 2 (SO 4 ) 3 +MuSO 4 + 2H 2 O. 

It remains to be seen whether the equation balances. This is easily 
determined by writing down in a column all the factors and elements 
that enter into the left hand side of the equation, and checking them 
off against those of the right-hand member, arranged in like manner. 

EXAMPLE B : Construct an equation showing the oxidation of 
ferrous sulphate to ferric sulphate by potassium permanganate. 

This reaction is carried out when it is desired to standardize a solu- 
tion of potassium permanganate by means of iron. 

The operation is as follows: 

In an appropriate flask 0.2 gramme of pure iron wire is dissolved in 
sulphuric acid. Into the resulting solution of ferrous sulphate, there is 
run a solution of potassium permanganate. The ferrous sulphate is 
changed to ferric sulphate, i.e., FeSO 4 becomes Fe 2 (SO 4 ) 3 . As long as 
this reaction continues, the permanganate of potassium solution is decol- 
orized. The instant when all of the FeSO 4 has been transformed into 
Fe 2 (SO 4 ) 3 the decomposition of the potassium permanganate ceases, and 
the solution is no longer decolorized. 

The number of cubic centimetres of the potassium permanganate 
solution used is noted, and this number is divided into the weight of 



CHEMICAL EQUATIONS AND CALCULATIONS. 95 

iron taken. The quotient expresses the value, iu iron, of one cubic 
centimetre of potassium permanganate solution. 
The substances entering into the reaction to be here considered, are: 
K 2 Mu 2 O 8 , 
FeSO 4 , 
H 2 SO 4 . 
The products resulting are: 

Fe 2 (S0 4 ) 3 , 
K a S0 4 , 
MnSO 4 , 
H 2 0. 

Therefore, there should be written, leaving space for the factors: 
K 2 Mn 2 8 + FeS0 4 + H 2 SO 4 = Fe 2 (SO 4 ) 3 + K 2 SO 4 -f- MnSO 4 + H 2 O. 

Regarding the change in the valence of the dominant element, the 
iron in the iron sulphate auxiliary equations are constructed which 
show that the iron passes from the dyad to the tetrad state. 
2FeO + O = Fe a 8 , 
Mn 2 O 7 = 2MnO + 5O, 
Two Fe require one O, 
One E 3 Mn a O 8 yields rive O. 

Therefore, 10 of a ferrous compound need 1 of the permanganate. 
Hence the quantity of the substance oxidized and the one performing 
this oxidation must be so adjusted, that the gain in the valence of the 
former is equivalent to the loss in valence of the latter. Then the fac- 
tors are arranged for the other substances in accordance with the pre- 
scribed conditions of the solution, acid, alkaline, or neutral, and the 
equation is balanced. 

Following these directions, there is obtained: 

K,Mn 2 6 + 10FeS0 4 -f 8H 2 SO 4 

= 5Fe 2 (S0 4 ) 3 -f K 2 SO 4 + 2MuSO 4 + 8H 2 O 

and, testing this reaction to see whether it is a true equation: 
In first member. In second member. 



K 


2 


2 


K 


Mu 
O 


2 

80 


2.. 

80 


...Mn 

o 


s 

Fe 
H.. 


18 
10 
16 


18. 
10., 
16. 


....S 
,...Fe 
..H 



The factors all balance, and therefore the equation is correct. 



9G LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

The chief advantage of this method of working out equations 
of oxidation and reduction, lies in the fact of its insuring a 
thorough acquaintance with the chemical nature of the 
changes involved in reactions of this kind. 

The Method of Negative Bonds. A convenient process of 
constructing equations of oxidation and reduction, is the so- 
called method of negative bonds.* 

A meaning different from the sense in which the word is 
generally accepted, is assigned to the term bond by this writer. 
According to him, by the bond of an element there is meant 
the amount of oxidation it is capable of sustaining, and hence 
his definition of a bond as " oxidizing force/' and the state- 
ment that, " when an element has no oxidizing force or power, 
it has no bonds/' and that, " when its only capacity is that of 
a reducing agent, its bonds are represented by a negative 
number." 

Among the rules given for ascertaining the number of 
bonds of an element, are the following : 

1. Hydrogen in combination always has one bond, which is 
always positive (H 1 ). 

2. Oxygen always has two bonds, and they are always 
negative (0 ~ n ). 

3. Free elements have no bonds; thus, metallic lead (Pb). 

4. The sum of the bonds of any compound is always equal 
to zero. Thus, H'N + V 3 - VI = 0. 

5. Acid radicals are always negative. Thus, 

H I I V 3 - VI = 0, or, Pb 3 VI (P0 4 ) 2 ~ VI = 0, 

the bonds of the radical being equal to the number of atoms 
of hydrogen with which it is capable of combining. 

* Otis Coe Johiisou, Negative Bonds and Rules for Balancing Equa- 
tions. Chemical News, 1880, Vol. XLII. p. 51. Also, A Study of Oxi- 
dation and Reduction. Appendix to Douglas & Prescott: Qualitative 
Chemical Analysis. Third Revised Edition, 1881. 



CHEMICAL EQUATION'S AKT) CALCULATIONS. 97 

6. Metals iu combination are usually positive. The most 
prominent exceptions are their compounds with hydrogen: 
Sb- ra H, +ra . 

Furthermore, as the oxidation of one substance must involve 
the reduction of some other, the number of bonds gained by 
the one, is lost by the other. 

From these principles a rule is derived for writing equa- 
tions of oxidation, if the products formed, are known. The 
rule is: "The number of bonds changed in one molecule 
of each, shows how many molecules of the other must be 
taken," the words each and other referring respectively to 
the oxidizing and the reducing agent. 

Applying this method to the problem before considered : 

K 2 Mn 2 O s + FeSO 4 -f H.,80, = Fe 2 <SO 4 ) 3 + MuSO 4 -f- K 2 SO 4 -f H 2 O. 

Mn a in the first member has 14 bonds. 

Mn 2 in the second member has 4 bonds. 

Loss = 10. 

Therefore the factor of FeSO 4 is 10. 

Fe in the first member has 2 bonds. 

Fe in the second member has 3 bonds. 

Gain = 1, 

and the factor of K 2 Mn 2 O 8 therefore is 1. 

The amount of H 2 SO 4 needed, must be determined according to the 
prescribed condition of the solution. 

The Algebraic Method. Methods resting on algebraical 
principles have also been devised for the constructing of 
chemical equations.* 

To illustrate these, the former problem is here solved 
once more: 



*J. Bottomley, Chemical News, 1878, Vol. XXXVII. p. 110. 
Schwauert, Lehrbuch der Pharmaceutischen Cliemie. 



98 LECTURE-XOTES OX THEORETICAL CHEMISTRY. 

K 2 Mu 2 O 8 -f 6FeSO 4 -f cII 2 8O 4 



-f 2Fe 2 (SO 4 ), 

(1) a = x; 

(2) 2a = y- 

(3) Sa + 4b + 4e = 4(K + 4y + l&+'w', 

(4) b = 2^; 

(5) j _|_ c = z + y + 3 2 ; 

(6) 2c = 2w. 
Substituting in (3), 

8 -f 46 -f 4c = 4^ + 8a + Qb + c\ or, 

(7) 3c = 4a + 26. 
And also: 

From (4) b = 2z, and 



c = a? + y + z, and 
" (1) and (2) 

c = a -f 2 + i&. 
Multiplying by 4, 

(8) 4c = 12a + 25. 
Combining (7) and (8): 

(7) 3c = 4a + 26 

(8) 4c = 12 + 26 



From (7) 6c = 8a + 46 
" (8) 6c = 18 + 36 

= _ 
Whence : 

aj = a; 



6 = 10a; 

c = 8a; 
and therefore: 
K a Mn 8 O e -I- 10FeS0 4 + 8H 2 SO 4 

= K 2 S0 4 + 2MnS0 4 + 5Fe 2 (SO 4 ) 3 + 8H 2 O. 

As will be seen, in this method the whole matter resolves 
itself into the solving of a set of simultaneous equations. 



CHEMICAL EQUATIONS AND CALCULATIONS. 99 



Calculation of Chemical Problems. , 

In studying chemical reactions, a variety of problems pre- 
sent themselves for consideration. 

Many of these offer no difficulty whatever, and perhaps 
can be most conveniently solved by expressing the reaction in 
the form of an equation and then making a proportion : 

As the symbol (formula) of the substance given, is to the 
symbol (formula) of the substance required, so is the weight 
of the substance given, to the weight of the substance 
required. The antecedents of the proportion must of course 
represent similar terms. 

Substitute the numerical values for the symbols (formulae), 
and solve the proportion in the usual manner. 

Calculation of the Molecular Mass of a Substance. 

A. Given: 

The formula; 
The atomic masses. 

EXAMPLE : Calculate the molecular mass of CaCO,. 



Atonic Mass. 

Ca 1 X 40 40 

C 1 X 12 12 

O 3 X 16 48 

Molecular mass = 100 

B. Given: 

The weight of one constituent in a given weight 
of a compound ; 

The total atomic mass of that constituent in the 
compound. 

EXAMPLE : Calculate the molecular mass of ethylic iodide from the 
following data : 



100 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

7.5 grammes of this substance contain 6.106 grammes of iodine. The 
total atomic mass of iodine in one molecule is 127. 

I : x : : 6.106 : 7.5 
127 : x :: 6.106 : 7.5 
* = 156. 

That is, the molecular mass of ethylic iodide is 156. 

Calculation of the Amount of any Constituent in a Compound. 

EXAMPLE : How much S is contained in 1.230 grammes of FeS ? 

FeS : S :: 1.23 : x 

88 : 32 :: 1.23 : x 

x = 0.4475. 

That is, in 1.23 grammes of FeS there are 0.4475 gramme of S. 

The calculation of the amount of any group or radical in a 
compound, is of course effected in a similar manner. 

EXAMPLE : How much CO 2 is contained in 5.530 grammes CaCO 3 ? 

CaCOs : CO 2 : : 5.530 : * 

100 : 44 : : 5.53 : x 

x = 2.4332. 

That is, 5.530 grammes of CaCO 3 contain 2.4332 grammes of CO a . 

Calculation of the Amount of a Compound which can be 
produced from a Given Amount of any of its Constituents. 

Given: 

The molecular mass of the compound; 
The total atomic mass of the constituent in a mole- 
cule of the compound. 

EXAMPLE : How much H 2 SO 4 can be made from 17.50 grammes of S ? 

S : H 2 SO 4 : : 17.50 : x 
32 : 98 : : 17.50 : * 
x = 53.594. 

Hence, 53.594 grammes of H 2 SO 4 can be made from 17.50 grammes 
of S. 



CHEMIC A L EQUATIONS 'AJTO ' CALtrSfa '' 10 1 

Calculation of the Percentage Composition of a Compound 
from its Formula. 

EXAMPLE: Calculate the percentage composition of ethyl alcohol from 
its formula C 2 H,O. 

Number of Atoms 
in the Molecule Atomic Mass. 

C 2 X 12 = 24 

H 6 1 6 

O 1 X 16 16 

Molecular mass = 46 
Then, making the proportion: 

Molecular mass : Total atomic mass : : 100# : x $ of each constituent, 
and applying this formula in turn to all constituents: 

Per cent. 
C 46:24 :: 100: r or = 52.18 

H 46 : 6 : : 100 : .c = 13.04 

O 46 : 16 : : 100 : x x- 34.78 

Calculation of the Chemical Formula of a Compound from 
its Percentage Composition. 

a. Calculation of the empirical formula. 

b. Calculation of the molecular formula. 

These methods of calculation have been fully explained in 
a previous chapter, to which reference should be made. 

But, in considering problems of this type, there is one form, 
which calls for special consideration. It relates to the, 

c. Calculation of the formulae of minerals. 
In mineralogy, formulae like : 

R"C0 3 , 
RO.CO,, 

R".Si0 3 , 
RO.SiO,, 

are frequently employed. 

These formulae mean, that basic radicals of the same class 
may replace each other to an undetermined extent, and yet 
represent a type of mineral identical in respect to crystalline 



102 L^OTUR^-KOTES "OH* THEORETICAL CHEMISTRY. 

form, and other physical properties. Groups of minerals 
answering this description, are called isomorphous groups. 
Their formulae are determined by the so-called oxygen ratio, 
which is found by calculating the percentages of oxygen 
present in the bases of the same type, considering the bases as 
anhydrous oxides, and the percentage of oxygen in the acid 
anhydrides, and comparing these values. 

In Dana's Mineralogy, for instance, the two following 
analyses are quoted for siderite, which, theoretically is FeC0 3 : 

Constituents. A. B. 

C0 2 = 38.35 per cent. 38.85 per cent. 

FeO =55.64 " 47.20 " 

MnO = 2.80 " 8.34 

MgO = 1.77 " 3.78 

CaO = 0.92 " 0.63 " 

Calculating the percentages of oxygen : 

A. B. 

in C0 2 - 27.890 28.254 

" " FeO = 12.340 1O489 

MnO = 0.631 1.879 

" MgO = 0.708 1.512 

CaO = 0.263 0.180 

The sum of the oxygen in the basic anhydrides is respect- 
ively : 

For A, 13.942; 
" B, 14.060. 

Comparing the percentages of oxygen in the C0 2 with that 
in the basic anhydrides, the ratio in both cases is essentially 
as 2 : 1. 

Hence the type formula of this mineral is written as RO.CO a 
or as R"C0 3 . 



CHEMICAL EQUATION'S AND CALCULATIONS. 103 

Formulae of a similar kind are constantly used to indicate 
the composition of silicates. 

These silicates may consist of metals of any valence, i.e., of 
monads, dyads, tetrads, etc., in combination with silica, Si0 2 . 

In these instances a concise formula could probably not be 
obtained if the ordinary methods of calculation were used, but, 
on replacing the weight of any constituent by an equivalent 
weight of some other substance isomorphous with it, a simpler 
relation among the constituents is readily established. 

The following will illustrate: 

A Swedish garnet yielded on analysis: 

Si0 2 = 36.62 
Al,0, = 7.53 
Fe a O, = 22.18 
CaO = 31.80 
MgO = 1.95 



100.08 

Among the constituents of this mineral, the iron and the 
aluminium, on the one hand, and the calcium and the magne- 
sium, on the other, are possessed of respectively the same 
valence. 

The iron sesquioxide can therefore be replaced by an 
equivalent amount of aluminium sesquioxide, or vice versa, 
and, in the same manner, an equivalent amount of calcium 
oxide can be made to replace the magnesium oxide deter 
mined by analysis, or vice versa. Thus: 

Fe 3 3 : A1 3 3 :: 22.18 :x 
160 : 102 :: 22.18 : x 

a? = 14.14. 

MgO : CaO :: 1.95 : x 
x = 2.73 CaO. 



104 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

These numbers express that 14.14 -(- 7.53 parts of Al,0 3 , 
i.e., a total of 21.67 parts of A1 2 3 , are equivalent to a mixture 
of 7.53 parts of A1 2 3 and 22.18 parts of Fe 2 3 , and that 
2.73 -f 31.80 parts of CaO, i.e., a total of 34.53 parts of CaO, 
are equivalent to 31.80 parts of CaO and 1.95 of MgO. 

The numbers thus obtained are : 

Si0 2 = 36.62, 

A1 2 3 = 21.67, 

CaO = 34.53. 

Proceeding now as in any other instance of the calculation 
of a formula from percentage composition, a simple ratio is 
obtained between the constituents. 

SiO, = 36.62 -4- 60 = .60 = 3, 

A1 2 3 = 21.67 -T- 102 = .20 = 1, 

CaO = 34.53 ~- 56 = .60 = 3. 

The result of course will be the same if the percentages 
are divided by the molecular masses, and the amounts of the 
oxides which are isomorphous, are then added together. 
Thus: 

Si0 2 - 36.62 -f- 60 = 0.6103, 

A1 2 3 = 7.53 -4- 102 = 0.0738, 

Fe 2 3 = 22.18 -s- 160 = 0.1380, 

CaO = 31.80 -f- 56 = 0.5678, 

MgO = 1.95 -s- 40 = 0.0487. 

Adding respectively the values for A1 2 3 and for Fe 2 3 , and 
the values for CaO and for MgO, there results : 

Si0 2 = 0.6103 = 3, 

(Al 2 3 .Fe 2 3 ) = 0.2118 = 1, 

(CaO.MgO) = 0.6165 = 3; 



CHEMICAL EQUATIONS AND CALCULATIONS. 105 

which result is the same as that previously obtained. The 
formula of the mineral as derived from these data can be ex- 
pressed as : 

3(CaMgO),(Al 8 Fe s O,),3SiO,, 
or as: 

(CaMg),(Al,Fe 1 )Si 1 O ia . 

In accordance with the custom of mineralogists, who prefer 
to represent the formulae of such minerals even more concisely, 
the letter R can be used to denote metallic radicals, and 
Roman numerals placed above the same, can be made to indi- 
cate the valence of the radicals : 

The above formula would thus be written: 

II VI IV 

E s (RJSi 1 0, 1 , 

a shorter, and an equally correct expression of the composition 
of this mineral. 

A formula of this kind can easily be changed to a formula 

ii 
in the old dualistic system, by converting R into RO and 

VI 

(R 2 ) into R 2 3 . It would then read : 

3RO,R 2 3 ,Si 3 6 . 

Comparing now the quantities of oxygen in combination 
with the several bases and with the silicon, it will be seen 
that they bear to one another the relation 3:3:6; that is, 
as 1 : 1 : 2. This ratio, in this instance 1 : 1 : 2, is termed 
the oxygen ratio, and it will be noticed that it is the same 
as the ratio of the total valence, the so-called atomic ratio, 
of each radical in the formula: 

II VI IV 

R,(RJSi,. 



106 LECTURE-XOTES ON THEORETICAL CHEMISTRY. 

For, 

II X 3 = 6; 

VI X 1 = 6; 
IV X 3 = 12. 

and 6 : 6 : 12, is the same ratio as 1 : 1 : 2. 

If it be required to calculate the miueralogical formula of 
a silicate from its percentage composition, tho first step to be 
taken will be the calculation of the atomic ratio. 

This is readily effected by observance of the following rule : 

Divide the percentage composition of each constituent by 
its atomic mass, multiply by its valence, and deduce the 
ratio from the resulting numbers. 

EXAMPLE. The percentage composition of pyroxene is given as : 

FeO = 8. 00 per cent. 
CaO =24.90 " " 
MgO = 13.40 " " 
Si0 2 = 53.70 " " 

Calculate the mineralogical formula. 
Proceeding as directed, 

FeO 8.0 -*- 72 = 0.111 X II = 0.222 
CaO 24.9 -4- 56 = 0.446 X II = 0.892 

MgO 13.4 -i- 40 = 0.335 X II =0.670 

1.784 
SiO a 53.7 -5- 60 = 0.895 X IV = 3.580 

and the ratio is therefore, 

1.784 : 3.580 
that is, as 1 : 2. 

Having thus obtained the atomic ratio, multiply this ratio by some 
number which will make the products divisible by the valence of the 
several classes of radicals, and then divide by the valence of the re- 
spective radicals. 

The atomic ratio in this problem was found to be: 

ii n> 
R, Si a . 



CHEMICAL EQUATIONS AND CALCULATIONS. 107 

Multiplying through by 2, and dividing by the valences II and IV 
respectively, there is obtained : 

1X2 2x2 

II IV 

Tf IV 

1 : 1 

and the mineralogical formula of pyroxene is therefore: 

RO, Si0 2 . 

Methods of Indirect Analysis. 

The quantitative determination of certain constituents in 
substances, is sometimes effected by methods of indirect an- 
alysis. 

As an illustration of these methods, the following types will 
be considered: The residue method, the substitution method, 
and the method which is based on numerical differences 
between molecular masses. 

I. The Residue Method. The substance is chemically acted 
upon by a reagent which is added in known quantity, but in 
excess. This excess is determined, and the amount of the 
substance sought is calculated from the data thus obtained. 

EXAMPLE. Calculate the amount of CO 2 in a sample of impureCaCOs 
from the following data: 0.305 gramme CaCO 3 were dissolved in 35 c. c. 
of normal HNO 3 . The HNO 3 which remained uncombined was neu- 
tralized by a solution of normal NaOH, of which 30.0 c. c. were used. 

Total HNO 3 = 35.0 c. c. 

HNO 3 neutralized by NaOH = 30.0 c. c. 

HNO 3 neutralized by CaCO 3 = 5.0 c. c. 

1 c. c. normal HNO 3 = 0.063 HNO 3 . 

5c.c. " " = 0.315HNO,. 

2 HN0 3 + CaC0 3 = Ca(NO 8 ) a + CO 2 -f H 3 O. 
2HN0 3 : CO 2 :: 0.315: x 
126 : 44 : : 315 : x 
x = 0.110 gramme CO 2 . 
0.305 : 0.110 :: 100 :a> 



108 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

II. The Substitution Method. The substance to be deter- 
mined is replaced by an equivalent amount of some other 
substance, which is directly determined, and from this the 
value sought is then calculated. 

EXAMPLE. Determine the strength of a solution of chlorine from the 
following data: 

A solution of potassium iodide was added in excess to 100 c. c. of the 
chlorine solution. A standard solution of Na 2 S 2 O 3 was used to deter- 
mine the iodine which was set free, and 50 c. c. of the Na a S 2 O 3 (sodium 
thiosulphate) solution were used. 

1 c. c. Na 9 S a Oa' solution ............... , ____ = 0.01268 I. 

50c. c.Na 2 S 2 3 " .................... = 0.634001. 

Hence 0.6340 gramme iodine was liberated. 

Atomic mass of I ......................... = 126.8 

" " Cl .......................... = 35.5 



I : Cl : : 0.6340 : x 

126.8 : 35.5 : : 0.6340 : x 

x = 0.1775. 

Hence 0.1775 gramme of chlorine is contained in 100 c. c. of the 
chlorine solution, and 1 c. c. of the solution contains 0.001775 gramme 
of chlorine. 

III. The Method based on Numerical Differences between 
Molecular Masses. Two divisions of this method must be 
recognized : 

A. The components of the mixture have one constituent 
in common. 

B. The components of the mixture have more than one 
constituent in common. 

A. In a mixture of two salts which have one constituent in 
common and which differ in their molecular masses, the com- 
mon constituent and the combined weight of the two salts 
are determined, and from these data the amounts of the 
other constituents are calculated. 



CHEMICAL EQUATIONS AKD CALCULATIOKS. 109 

EXAMPLE 1. Mixed Silver Salts. Given, the weight of a precipitate, 
consisting of the mixed chloride and bromide of silver, and the weight 
of the silver therein contained. Required, to calculate the proportions 
of chlorine and bromine in the sample. 

If the common constituent be calculated to its combination with the 
element or group having the lowest atomic or molecular mass, the figure 
obtained will fall short of the given amount of the mixed salts, by an 
amount proportional to the excess of the higher combining mass over 
the lesser. 

AgBr -j- AgCl = 0.75 ; Cl atomic mass = 35.5 ; 
Ag therefrom =0.50; Br " " =80. 

Calculating all the Ag to its equivalent of AgCl : 

Ag : AgCl : : 0.50 : x 
108 : 143.5 : : 0.50 : x 
71.75 = 108-c 
0.6643 = x. 
Then, 0.7500 

less 0.6643 



0.0857 excess due to Br. 
Br - Cl : Br : : .0857 : x 
44.5 :80 : : .0857 : x 
6.8560 = 44.5z 
0.1540 = x. 
Hence, the Br = 0.1540. 

0.7500 is the total amount of the mixed silver salts. 

Ag = 0.5000 

Br --= 0.1540 

Ag -|- Br = 0.6540 

0.7500 
less 0.6540 



Cl = 0.0960 

Hence, Ag present = 0.5000 
Br " = 0.1540 
Cl " -= 0.0960 



110 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 
The results may be thus verified : 

Br : AgBr : : 0.154 : X 

80 : 188 : : 0.154 : x 

28.952 = 80z 

0.3619 = x. 

.% AgBr = 0.3619. 

Cl : AgCl : : .096 : x 
35.5 : 143.5 : : .096 : x 
13.776 = 35. 5x 
0.3881 = x. 
.-. AgCl = 0.3881. 

Hence, AgBr = 0.3619 

AgCl = 0.3881 

Total AgCl -f AgBr = 0.7500 

EXAMPLE 2. Mixed Sulphates. Given, the weight of a precipitate con- 
sisting of the mixed sulphates of potassium and sodium, 0.371 gramme. 
SO 3 present therein, 0.200 gramme. Required, the amount of Na 2 O 
and the amount of K 2 O in the sample. 

Calculating all the SO 3 to its equivalent of Na 2 SO 4 : 

S0 3 : Na a S0 4 : : 0.200 : x 
80 : 142 : : 0.2 : x 
28.4 = 80* 
0.355 = x. 

that is, all of the SO 3 present would be equivalent to 0.355 Na a SO 4 . 
Subtracting tiiis from the total of the mixed sulphates : 

0.371 - 0.355 = 0.016, 

which amount is due to the higher atomic mass of the potassium. 
Hence, 

K 2 O - Na 2 O : K 2 O : : .016 : x 
32 :94 :: .016 :x 
1.504 = 32z 
0.047 = x. 



CHEMICAL EQUATIONS AND CALCULATIONS. Ill 

Hence, the KO 2 present is equal to 0.047, and: 



0.371 
0.247 

Na a O present = 0.124 
To check the results obtained: 



K 2 : K 2 SO 4 : : 0.047 : x 
94 : 174 : : 0.047 : x 

8.178 = 94z 
0.087 = x. 

That is, K 2 SO 4 =0.087. 

Na 2 O :Na 2 SO 4 : : 0.124 : x 
62 : 142 : : 0.124 : * 
17.608 = 62z 
0.284 = x. 

That is, Na 2 S0 4 = 0.284. 

K 2 SO 4 = 0.087 
Na 2 S0 4 = 0.284 



Total mixed sulphates = 0.371 

B. In a mixture of two salts which have more than one 
constituent in common, the amounts of these common con- 
stituents are determined and then calculated to their respec- 
tive combinations. 

This class of problems can be readily solved by arithmetic, 
but perhaps even more conveniently by algebraic methods, as 
the following will show : 

EXAMPLE. Iu a sample of commercial bicarbonate of soda there are 
present : 

Sodium oxide = 32.00 per cent. 
Carbon dioxide =45.00 " 



112 LECTURE-XOTES OK THEORETICAL CHEMISTRY. 

Calculate the amount of sodium monocarbonate and of sodium bicar- 
bonate in the sample. 

Sodium monocarbonate Na 2 CO 3 = Na 2 O -[- CO a . 
Sodium bicarbonate 2NaHCO 3 = Na 2 O -j- 2CO 2 -f H 2 O. 

The first step to be taken is to calculate all theNa 2 O to its equivalent 
in CO 2 : 

Na 2 O : CO 2 : : :32.0 : x 
62 : 44 : : 32.0 : * 
x = 22.7096CO,. 

This amount of CO 2 would be required to transform all of the Na 2 O 
into Na 2 CO 3 (monocarbouate), but as the main portion of the sodium 
oxide is present in the form of NaHCO 3 (bicarbonate), there is needed 
this amount of CO 2 , 22.7096 per cent, and as much more as is necessary 
to form the bicarbonate. 

As 2NaHCO 3 = Na 2 O -f 2CO 2 -f H 2 O, the difference between the 
total CO 2 in the sample, and the above amount, 22.7096 per cent, must 
be multiplied by 2, and this product calculated to sodium bicarbonate. 
Thus : 

Total CO 2 in sample, 45.0000 per cent, 
less 22. 7096 



22.2904 per cent. 

22.2904 X 2 = 44.5808 

C0 2 : NaHC0 3 : : 44.6 : x 

44 : 84 : : 44.5808 : * 

x = 85.108 per cent. 

Hence, NaHCO 3 = 85.1100 

Total CO 2 = 45.0000 
a combined in the form of bicarbonate = 44.5808 



CO 2 = 0.4192 
which must be calculated as present in the form of monocarbonate. 

CO 2 : Na 2 C0 3 : : 0.4192 : x 
44 : 106 : : 0.4192 : x 
x - 1.01. 



CHEMICAL EQUATIONS A2?D CALCULATIONS. 113 

Hence, Na 2 CO 3 = 1.01 per cent, 

and the sample therefore contains: 

NaHCO 3 =85.11 per cent, 
Na,CO 3 = 1.01 ' 

To prove the correctness of the results thus obtained, a check calcuia 
tion is easily made. Thus : 

Na,CO, : CO 2 : : 1.01 : x 
106 : 44 : : 1.01 : x 

x = 0.41. 

NaHCO, : CO 2 : : 85.11 : x 
84 : 44 : : 85.11 : x 
x = 44.59 ; 

that is, 

CO 2 in form of Na 2 CO 3 = 0.41 
CO 2 " " NaHCO 3 = 44.59 

Total = 45.00 

which corresponds to the amount as found by analysis. 
The same problem can be solved by algebra in the following manner: 

CO 2 = 45.00 per cent, 
Na a O = 32.00 " 

Let x percentage of Na 2 CO 3 ; 

y - 

Then, 

r(\ ro 

= 45 




Na 2 C0 3 ' 2NaHC(V 
Substitute the molecular masses in their proper places, and solve for y. 
y = 85.11 



114 LECTURE-tfOTES ON THEORETICAL CHEMISTRY.- 

Hence, NaHCO 3 = 85.11 percent. 

85.11 :*: : 2NaHCO 8 : Na 3 O 
85.11 :x :: 168 : 62 

* = 31.41 per cent Na 2 O present as NaHCO 

Total Na a O in sample = 32.00 
Na 2 O present as NaHCO 3 = 31.41 

Na 2 O " " Na 2 CO 3 = 0.59 

Na 2 O : Na 2 CO 3 : : 0.59 : x 
62 : 106 : : 0.59 \x 
x = 1.01 per cent. 



Hence, the sample contains: 



NaHCO 3 =85.11 per cent 
a a C0 3 = 1.01 



VOLUME AKD WEIGHT RELATIONS OF GASES. 1 15 



CHAPTER VIII. 
VOLUME AND WEIGHT RELATIONS OF GASES. 

Volume Relations of Gases. The ratio of weights of equal 
volumes of elements, in the form of gas, is the same as the 
ratio of their atomic masses. Exceptions to this are the ele- 
ments zinc, mercury, cadmium, phosphorus, and arsenic, 
which will be considered later. Thus : 

One litre of : weighs : Atomic Mass. 

Hydrogen 0.0896 gramme 1 

Oxygen 1.4295 grammes 16 

Nitrogen 1.2555 " 14 

From these figures it appears that, weighing equal volumes, 
oxygen weighs about sixteen times as much, and nitrogen 
about fourteen times as much, as hydrogen. 

Strictly speaking, 1.4295 is only 15.9 times 0.0896, and 
1.2555 is a trifle over 14 times 0.0896, but the unavoidable 
errors of experiment will account for these differences. 

One litre of hydrogen weighs 0.0896 gramme. This value 
is termed a crith, and therefore one litre of hydrogen is said 
to weigh one crith. As oxygen weighs sixteen times as much 
as hydrogen, one litre of oxygen is said to weigh 16 criths, 
one litre of nitrogen weighs 14 criths, and so on. 

The following table, prepared by the writer, may prove 
convenient for reference in calculations concerning gases. 



116 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 



2-8.23! 



**!~.2S 



i-iCDO^CDOSO^aO^^O5^O 
^ 05 CO -H GO J> O ^t< CO t- O - 
Oi " 1O CO GO Oi "^ 
O5 OO GO 00 <M G<3 







1. 



o 



ll^is 



i^ 



*3 
. ce 

SJ . 

II* 



I IllllililSllllllll'lllil 



CO O O 

g^s5 



OTHTHOOOC--JOOT^05(MTH 



1> CO O CD 
{>-^'^t | T- 1 t~- 
O-"JOS^J>COOi 

r-J o ^' GO* ^ CD' os GO o 



"<^COGOGOI>COO5COC50O1OCDJ>GO-^O530CO'<^OCOO <00 
i-HOi ^COt>T-i<MCOCOC5CO<MTHCOr-iTHCDWCDO^HT^ 







VOLUME AND WEIGHT RELATIONS OF GASES. 117 

S& 



' a o=s a 

*- 5 iS?! 




^ ,_, ,33" ,_; T_; s<i 10 ,_, t-' co' ci od i- so o 



i i 






tiCCO 



1C t- 1-1 5? 

OO Ct CO O5 

o <M yi o TH oi 



C> QOCOOO 



OOOOO1COOOOO 
























a--i 1 

^ 6 6 S 

1 o o fe 





5 



f i 



c c ^ o o 

8 E g 8 



s -o -c 



b x 



1 s 



-31! 

8 S g g 



II 



o S 

8Sf s 



inch 
cubic 



|i| 



a c 

S S 

3 3 

"3 O 

O O 

= C 



QO 

1! 



SgJ 

2|l 

2 



c 

<c ^ 



= .S .5 .S 



III! 



118 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

The exceptions before referred to, when it was stated, that 
the ratio of weights of equal volumes of elements in the gas- 
eous condition are the same as the ratio of their atomic 
masses, are zinc, cadmium, mercury, phosphorus, and arsenic. 

One litre of : iveiglis : Atomic Mass. 

Zinc as gas 2.9344 grammes 65.5 

Mercury " " 9.0199 " 200 

Cadmium" 5.0944 " 112 

2.9344 -f- 0.0896 = 32.75 
9.0199 -f- 0.0896 = 100.66 
5.0944 -T- 0.0896 = 56.85 

or, in the cases of Zinc, 

Mercury I xt 1S P ractica % one nalf tneir 
Cadmium, J atomic masses ' 

One litre of: weighs: Atomic Mass. 

Phosphorus as gas 5.7150 grammes 31 
Arsenic " " 13.1886 " 75 

Therefore, in the case of these elements, 

5.7150 4- 0.0896 = 63.78 
13.1886-^0.0896= 147.19, 

it is practically equal to twice their atomic masses. 

Excepting then, zinc, mercury, cadmium, phosphorus, and 
arsenic, it has been found that when the elements in gaseous 
form are made to combine, two volumes of gas always result; 
no matter what may be the number of volumes that enter 
into the compound, they invariably become condensed into 
two volumes. Thus : 

1 vol. H and 1 vol. Cl form 2 vols. HC1; 
2vols. H " 1 " "2 " H 2 0; 
3 " H u 1 " N " 2 " NH 8 . 



VOLUME AND WEIGHT RELATIONS OF GASES. 119 

Compound gases in forming chemical combinations, behave 
in the same manner. Thus : 

2 volumes CO + 1 volume 2 = 2 volumes C0 3 . 
In the case of zinc, mercury, and cadmium, 

2 vols. Zn -f 2 vols. Cl = 2 vols. ZnCl,; 
2 Hg+2 Cl = 2 HgCl,; 
2 Cd+2 Cl = 2 CdCl,. 

and in the case of phosphorus and arsenic, 

| vol. P + 3 vols. H = 2 vols. PH 3 ; 
4 " As + 3 H = 2 " AsH 3 . 

From these data there may be deduced the : 

Law of Volumes first advanced in 1805 by Gay-Lussac 
and Von Humboldt. This law reads: 

The ratio in which gases combine by volume is always a 
simple one, and the volume of the resulting gaseous product 
bears a simple ratio to the volumes of its constituents. 

A careful consideration of the data above recorded, warrants 
the following more precise formulation of the law : 

The combining volumes of all elementary gases are equal, 
excepting those of zinc, mercury, and cadmium, which are 
twice those of the other elements, and of phosphorus and 
arsenic, which are one half. 

This law of volumes, originally discovered through direct 
experimental research, has lately, by Clan sins, been shown to 
be most readily deduced from the law of Avogadro (1811). 

Avogadro's law holds that : 

Equal volumes of all gases contain the same number of 
molecule.-. 

This law has not only been proved true by mathematical 



120 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

reasoning, but its correctness is affirmed by every known 
chemical and physical phenomenon having any bearing on 
the case. 

The number of molecules in equal volumes being the same, 
if the molecules were diminished in number, these volumes 
would, of course, be diminished proportionally. 

Neglecting for the present the exceptions noted (Zn, Hg, 
Cd, P, As), a molecule of any element in the gaseous condi- 
tion can be assumed to consist of at least two atoms. 

To illustrate this : Consider a litre selected as the unit of 
volume; consider also that it is possible to count the number 
of molecules in any given space, and further assume, that a 
litre contains one million molecules. 

From the law of volumes it is known, that one litre of 
hydrogen, assumed to contain one million molecules of hydro- 
gen, will combine with one litre of chlorine, assumed to 
contain one million molecules of chlorine,, to form two litres 
of hydrochloric acid gas, containing two million molecules of 
HOI. 

As the resulting gas contains two million molecules, each 
molecule of which contains hydrogen, each one of the original 
one million molecules of hydrogen must have consisted of, at 
least, two equal particles. 

The same reasoning applies to the chlorine gas, and this 
demonstration will hold good, whatever number of molecules 
may be assumed as existing in a given space. 

Again : Two litres of hydrogen, assumed to contain two 
million molecules of hydrogen, will combine with one litre of 
oxygen, assumed to contain one million molecules, to form 
two litres of water vapor, assumed to contain two million 
molecules. 

Hence, in order to form two million molecules of H 2 0, 
each molecule containing oxygen, each of the one million 
molecules of oxygen taken, must have consisted of at least 
two particles atoms. 



VOLUME AXI) WEIGHT RELATIONS OF GASES. 121 

In the same manner it might be shown that each molecule 
of nitrogen must also consist of at least two particles, and, 
barring the exceptions noted, this argument might be applied 
to the entire list of elements obtainable in the form of gas. 

If equal volumes of two monad elements, which can com- 
bine chemically, are placed together under the proper con- 
ditions, chemical combination will ensue, and the resulting 
compound will, in volume, be equal to the sum of the volumes 
of its constituents. Thus: 

1 volume H 2 -|- 1 volume C1 2 = 2 volumes HC1, 

and, as equal volumes contain the same number of molecules, 
this statement can be thus formulated : 

1 molecule H -j- 1 molecule 01 = 2 molecules HOI, 

(2 atoms) (2 atoms) " (Each of 2 atoms. 

Total = 4 atoms.) 

No change in volume has taken place. 

If combination is to be effected between a dyad element 
and a monad element, each atom of the former requires two 
atoms of the latter. As the molecules of each element con- 
sist of two atoms, and as each molecule of the resulting com- 
pound consists of three atoms, there results : 

2 molecules H + 1 molecule = 2 molecules H 2 0. 

(Total of 4 (Total of 2 (Each of 3 atoms, 

atoms.) atoms.) Total = 6 atoms.) 

That is to say, three molecules have become condensed into 
two molecules, and as equal volumes contain the same num- 
ber of molecules, this fact can be thus stated : 

2 vols. H 2 + 1 vol. 2 = 2 vols. H 2 0. 

In an analogous manner, these relations can be reasoned 
out for triads, tetrads, etc., and also for the exceptions pre- 
viously noted. 



122 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

From what has been previously stated, it follows that to 
write correctly the symbol of an element when in the gaseous 
condition, its usual symbol must be doubled. Thus, when 
bromine is to be represented as a gas, its symbol should be 
written Br 3 and not Br; iodine as a gas should be expressed 
as I 2 ; and so on. 

Zinc, mercury, cadmium, phosphorus, and arsenic of course 
are exceptions. As the molecules of the first three are mon- 
atomic, their symbols, even when the elements are to be repre- 
sented as gases, are respectively Zn, Hg, and Cd. 

Phosphorus and arsenic, on the other hand, when in the 
gaseous condition, are expressed by P 4 and As 4 , respectively, 
because their molecules are tetra-atomic. 

All of these considerations lead to the conclusion that : 

The specific gravity of most elements in the gaseous con- 
dition is equal to their atomic mass,* and the specific gravity 
of compound gases is equal to one half their molecular mass. 

The simple relations by volume, obtaining in cases of com- 
bination and decomposition of gaseous bodies, are perhaps 
best illustrated by a few examples. 

EXAMPLES. 

(a) What volume of hydrogen is required to combine with 20 c. c. of 
nitrogen to form ammonia gas (JN"H 3 )? 
The formula of NH 3 shows that: 

1 vol. N 3 + 3 vols. H 2 = 2 vols. NH 3 . 

In this case, the volume of the nitrogen is given as 20 c. c. Substi- 
tuting the proper numerical equivalents in the above equation, there 
results: 

20 c. c. N 2 + 60 c. c. H a == 40 c. c. NH 3 . 

* Exceptions. The specific gravity of zinc, mercury, and cadmium, 
when in the gaseous condition is equal to one half their atomic mass ; 
the specific gravity of arsenic and phosphorus, when in the gaseous 
condition, is equal to twice their atomic mass. 



VOLUME AXD WEIGHT RELATIONS OF GASES. 1^3 

(6) What volume of mercury gas will combine with 182 c. c. of 
chlorine gas to form mercuric chloride? 

2 vols. Hg -f 2 vols. Cl a = 2 vols. HgCl 2 . 
The volume of the chlorine is given as 182 c. c. Hence, 
182 c. c. Hg -f 182 c. c. Cl a = 182 c. c. HgCl 2 . 

(c) How much oxygen is required to burn 219 cubic feet of hydrogen 
gas? 

2 vols. H 2 + 1 vol. O 2 = 2 vols. H 2 O. 

The volume of the hydrogen is given as 219 cubic feet. Hence, 
219 c. f. H 2 -f 109.5 c. f. O a = 219 c. f. H 2 O. 

(d) 22 litres of nitrogen trichloride were dissociated into the com- 
ponent gases. What was the volume of the mixed gases after dissocia- 
tion? 

2 vols. XC1, = 1 vol. N 2 -f 3 vols. C1 2 . 

The volume of the nitrogen trichloride is given as 22 litres. Hence, 
22 Is. NC1 3 = 11 Is. N 2 + 33 Is. C1 2 . 

(e) 125 c. c. of nitrogen gas and 210 c. c. of hydrogen gas can form 
what volume of NH S ? Which gas is in excess, and to what extent? 

1 vol. N 2 + 3 vols. H 2 = 2 vols. NH 3 . 

But the amount of nitrogen given is evidently more than sufficient to 
combine with the amount of hydrogen given. Therefore, as 210 c. c. 
= 3 vols., 1 vol. = 70 c. c., and therefore: 

140 c. c. of NH 3 will be formed, and 125 70 = 55 c. c. of N a will 
remain uncombined. 

(/) Given 630 c. c. arsenic gas and 840 c. c. chlorine gas. How much 
AsCl 3 can be formed; which gas, and how much of it, remains un- 
combined? 

vol. As, -}- 3 vols. Cl s = 2 vols. AsCl,. 



124 LECTURE-NOTES OX THEORETICAL CHEMISTRY. 

The arsenic gas is evidently in excess, for 630 is more than of the 
amount of chlorine given. 

The amount of chlorine must therefore be made the basis of calcula- 
tion. 

3 vols. = 840 c. c. 
i vol. = 140 c. c. 
Hence, substituting the proper numerical values in above equation: 

140 c. c. As 4 + 840 c. c. GV= 560 c. c. AsCl 3 . 

This is the amount of the AsCl 3 formed; the arsenic gas is in excess, to 
the extent of 630 140 = 490 c. c. 

Relation between Mass and Volume in Gases. 

Chemical equations, besides representing the relations by 
weight of the various factors concerned, exhibit also, as has 
been previously stated, the volume relations obtaining be- 
tween the different factors, when these are in the gaseous 
state. 

Thus the equation : 

not only illustrates the fact that one molecule of methane 
combines with two molecules of oxygen to form one molecule 
of carbon dioxide and two molecules of water, but it shows 
also, that one volume of methane and two volumes of oxygen 
combine to form one volume of carbon dioxide and two 
volumes of water vapor. 

The volume of any gas may be calculated from its weight, 
by dividing the latter by the weight of one litre of the gas or 
vapor; the quotient represents the volume in litres. 

The weight in grammes of one litre of any element in the 
state of gas or vapor, under standard conditions, is found by 
the formula: 

Weight = 0.0896 X atomic mass of the element.* 

* Of course in the case of zinc, mercury, and cadmium the formula 
reads, Weight 0.0896 X \ atomic mass; and in the case of phosphorus 
and arsenic, Weight O.C896 X 2 atomic mass, 



VOLUME AND WEIGHT RELATIONS OF GASES. 125 

In the case of compound gases, the formula: 

Weight = 0.089G x molecular mass, 

yields the desired result. 

An example will illustrate the solving of problems of this 
kind. 

EXAMPLE. Given, 2.5 grammes of hydrogen and 7.5 grammes of 
chlorine to form hydrochloric acid gas. What is the weight, and what 
is the volume of the product ? Which gas is in excess, and to what 
extent ? 

Cl : H : : 7.5 : x 

35.5: 1 : :7.5: x 

x = 0.2111. 

This shows that 0.2111 gramme of hydrogen is required to combine 
with 7.5 grammes of chlorine. 

Total hydrogen = 2.5000 grammes. 

Hydrogen required. . . = 0.2111 

Hydrogen in excess. . = 2.2889 " 
The weight of the HC1 formed is : 

7 5000 grammes. 

0.2111 

7.7111 

The volume of the HC1 is readily figured. 
The weight of one litre of HC1 is equal to: 

0.0896X1 mol. mass of HC1, 
0.0896X - = 1.6352 grammes. 

The weight of the HC1 produced is 7.7111 grammes, and this corre- 
sponds to: 

7.7111 -s- 1 .6352 = 4.715 litres. 

The weight of the excess of hydrogen is 2.2889 grammes, and this 
corresponds to: 

2.2889 -=- 0.0896 = 25.5245 litres. 



126 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

The sum of the atomic masses indicated by a chemical 
symbol or formula is proportional to the mass (weight) of the 
substances involved in a chemical reaction, be these masses 
(weights) given in criths, or in any other unit. To express 
this in a formula, let : 



, ! represent the molecular masses of any two substances. 



m 

m' 

n I represent the number of their molecules in a given re- 
n' } action. 



Then nm and n'm' represent the formulae of these substances. 
If IF" and W express weight in criths, then: 

nmin'm':: W:W. 

It will be remembered that the molecular mass of a body 
is equal to twice its specific gravity in the gaseous state, the 
specific gravity being referred to hydrogen as standard. 

Therefore, if molecular mass is represented by m', 

m' 2 sp. gr. 

The weight of a body is equal to the product of its volume 
by its specific gravity. 

If: weight = W, 

volume = v, 
specific gravity = sp. gr., 

W' = v x sp. gr. 
If in the proportion : 

nm: n'm':: W: W 
there are substituted the values: 

m' = 2 sp. gr. 
and 

W = v X sp. gr., 



VOLUME AND WEIGHT KELATIOXS OF GASES. 127 

there is obtained the expression : 

nm : n' 2 sp. gr. : : W : v X sp. gr. 
nm : 2n' : : W : v 
| nm : n' :: W : v. 

This formula permits the calculation of the volume of a 
gas or vapor involved in a chemical reaction, when the weight 
of some factor or product is known, and conversely, permits 
calculation of the weight, when the volume is given. 

This may be formulated by expressing the reaction in the 
form of an equation and then making the proportion : 

As one half the symbol (formula) of the substance whose 
weight is given or sought, is to the number of molecules of 
the substance whose volume is given or sought, so is the 
weight in criths of the first-named substance, to the volume 
in litres of the last-named substance. 

Numbers are then substituted for the respective symbols 
(formulae), and the calculation made as indicated. 

EXAMPLES. 

(a) What amount of potassium chlorate is required to yield 1 .75 litres 
of oxygen ? 

2KClO 8 = 2KCl-f 3O a . 

K2KC10 3 ) : 3 : : x : 1.75 
122.6:3 ::z:1.75 
3z = 214.55 
a? = 71. 517 criths 
71.517 X 0.0896 = 6.401 grammes. 

(b) How many litres of nitrous oxide can be obtained from 250.0 
grammes ammonium nitrate ? 

NH 4 NO 3 = 2H 3 O -f N S 0. 



40 : 1 : : 2790.18 : x 
(te = 2790.18 
x = 69.75 litres. 



['28 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 



Analysis of Gases. 

Introductory. Gas analysis is divided into ultimate and 
proximate analysis. In ultimate analysis the gaseous com- 
pound or mixture is burned, and the amounts of the elements 
present are calculated from the amount of H 2 0, of C0 2 , the 
amount of residual gas, and the change in volume produced 
by the combustion. 

In proximate analysis the various constituents of a gaseous 
mixture are absorbed by certain reagents, successively applied. 

The comparative amounts of the gases present, must, in 
both ultimate and proximate analysis, be measured before 
and after the operations indicated, and must be reduced to 
standard conditions. 

The values to be determined are, the volume of the gas, its 
absolute temperature, and its pressure. These values are 
respectively designated by F, 7 7 , and P. Different methods 
of gas analysis have been devised which base on the determi- 
nation of the one or the other of these values. 

In Regnault's method, for instance, P is measured, in 
Orsat's process F is determined; where the analysis is effected 
by the eudiometer and the absorption tube, F, T, and P, are 
recorded. 

Proximate Analysis. The apparatus generally employed 
for proximate analysis consists of a combination of three tubes 
which are all in connection, but the communication between 
which can be entirely shut off by stopcocks. A measured vol- 
ume of gaseous mixture is introduced into the so-called ab- 
sorption-tube. There it is treated successively with different 
reagents to remove the various constituents it may contain; 
the gas is remeasured after treatment with each reagent, and 
its volume noted. 

Thus, potassium hydrate removes carbon dioxide, sulphurous 
oxide and sulphuretted hydrogen; pyrogallate of potassium 



VOLUME AND WEIGHT RELATIONS OF GASES. 129 

removes oxygen; bromine removes the olefiants, cuprous 
chloride removes carbon monoxide, etc. 

If the gaseous mixture contains hydrogen, this will remain 
after removal of the constituents above named. 

A known volume of the hydrogen is transferred to a tube 
provided with two platinum wires or foils, an excess of oxygen 
is introduced, the mixture is exploded, and the residual volume 
of the gas is measured. 

From the data thus obtained, the percentage composition of 
the gaseous mixture is calculated. 

EXAMPLE : 1. Volume of gas used .................... 92.0 c. c. 

2. Volume after absorption of CO 2 ......... 89.0 c. c. 

3. Volume after absorption of CO .......... 69.0 c. c. 

4. Volume taken for estimation of hydrogen 58.0 c. c. 

5. Volume after addition of air ............ 93.0 c. c. 

6. Volume after combustion .............. 75.0 c. c. 

CO 2 = 92.0 
-89.0 

3.0 c. c. 
= 3.86 per cent CO,. 

CO = 89.0 
-69.0 
20.0 
= 31.74 per cent CO. 



Contraction on combustion : 

93.0 
75.0 

18.0 c. c. 

2 vols. H 2 -f 1 vol. O 2 = 2 vols. H 3 O. 

Two thirds of the contraction represents the volume of hydrogen 
present. 

The volume of hydrogen taken, is 58.0 c. c., therefore: 



12.0 X 69.0 X 100 

58.0X92 = 1.3 per c 8 ntH.. 



130 LECTURE-NOTES OK THEORETICAL CHEMISTR^* 

The percentage of uitrogen present is determined by adding the 
values calculated, and subtracting their sum from 100. 
The gas analyzed has therefore the following composition: 

CO 2 3.26 per cent. 
CO = 21.74 " 
H 2 = 15.52 " 

N 2 = 59.48 " 
100.00 

Method of Explosions. The composition of some gaseous 
mixtures can be effected entirely by the method of explosions, 
by what is termed, the indirect method. 

An explosion of combustible gases causes a diminution of 
volume. This contraction, the volume of CO, produced, and 
the original volume of the gas employed, are the only data 
necessary to calculate the composition of a gaseous mixture 
in an analysis of this kind. 

The contraction experienced by the different gases in com- 
bustion can be determined by experiment, or, it can be deduced 
from the law governing the combination by volumes. For 
instance : 

In the case of H^ : 

2 vols. H 2 -f 1 vol. 2 = 2 vols. H 2 0. 

But, unless the tube is kept at a temperature above the boil- 
ing-point of water, the water-vapor condenses and the gas all 
disappears. Therefore in this special instance: 

2 vols. -j- 1 vol. == 3 vols. become \ol. 

The loss in volume experienced is therefore 3 volumes. 

Two vols. of H 2 were employed, f 1.5; therefore the 
contraction is 1.5 times as great as the unit volume of the 
gas, hydrogen, which was exploded. 

In the case of CO : 

2 vols. CO + 1 vol. 2 = 2 vols. C0 2 , 
vols. -(- 1 vol. = 3 vols. become 2 vols. 



VOLUME AND WEIGHT RELATIONS OF GASES. 131 

The loss is therefore 1 volume. Dividing this loss by the 
number of volumes of the gas exploded, carbon monoxide, we 
have 1 -f- 2 = 0.5. The contraction therefore is % the unit 
volume of the gas exploded. 

In the case of 



1 vol. CH 4 + 2 vols. 2 = 1 vol. C0 2 + 2 vols. H 4 0. 

1 vol. -j- 2 vols. = 3 vols. become 1 vol., for the 2 vols. water- 
vapor condense. 

The loss is therefore 2 volumes, and the contraction is 
2-^-1 2. Hence the contraction is twice as great as the 
original volume of the gas represented. 

EXAMPLE:* If a mixture of hydrogen, carbon monoxide, and methane 
is to be analyzed, these gases can be respectively represented by x, y, 
and z. 

If the original volume of the gas is designated by A, the contraction 
by C, and the amount of CO S by D, then 



The values of x, y, and z must be calculated. 
To find x: 



(1) x = A - D 

To find y: 



= -ZC+ID 
- BA - 3D 



* From Sutton, Volumetric Analysis, 6th Ed., 1890. 



132 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 
To find 2: 

y + * = V 

z = D-y 



Substituting the values found by experiment in these three 
formulae, which give the values of x, y, and z, respectively, 
the amounts of hydrogen, carbon monoxide, and methane 
represented by these letters are easily calculated. 

The percentage composition of the gaseous mixture is 
ascertained by solving the following proportions: 

A : x : : 100 : per cent of H; 
A : y : : 100 : per cent of CO; 
A : z : : 100 : per cent of CH 4 . 

If the gas mixture contained nitrogen, this would be de- 
termined by exploding the residual gas, after removal of the 
C0 2 , with an excess of hydrogen. The contraction observed 
divided by 3, would give the volume of oxygen in the residue, 
and this deducted from the residue, would yield the amount 
of nitrogen. If A represents the original gas, and n the 
amount of nitrogen it contains, the expression A n would 
have to be substituted for A in the equations cited. 

Having ascertained the proximate constituents of a gaseous 
mixture, the amounts of the elements present, carbon, hydro- 
gen, nitrogen, etc,, can, of course, be very readily calculated. 



THE PERIODIC LAW. 133 



CHAPTER IX. 
THE PERIODIC LAW. 

Introductory. The fact that certain similarities exist be- 
tween the properties of some of the elements, has been known 
for a long time, and attempts to find connections between 
the general properties of such elements and their respective 
atomic masses, date back to about the first quarter of this 
century. 

Thus, Dobereiner, in 1829, noticed that in several in- 
stances an element possesses an atomic mass which is approx- 
imately the average of the atomic masses of two other 
elements which resemble it closely in their properties. 

For instance, the atomic masses of calcium, barium, and 
strontium are, respectively, 40, 136.9, and 87, the latter num- 
ber being approximately one half of the sum of the other 
two. Again, bromine has an atomic mass of 80, about one 
half of the sum of the atomic masses of chlorine 35.5, and 
of iodine 126.5. 

Dobereiner further found, that in some cases three ele- 
ments, which have analogous properties, possess atomic masses 
which are almost identical. Such groups are formed, for in- 
stance, by iron, cobalt, and nickel, and by platinum, osmium, 
and iridium. 

This investigator hoped that a systematic classification of 
the elements might be established on this basis, but a realizing 
of this wish was not possible, until careful analysis had fur- 
nished accurate determinations of tho atomic masses. 

Gmelin, Dumas, Cooke, Pettenkofer, Kremers, Odling, and 



134 LECTURE-KOTES ON THEORETICAL CHEMISTRY. 

Gladstone, among others, worked to the attainment of this 
end, but the periodic law, as it is now established, is due 
chiefly to the labors of Newlands, Mendeleeff, and Lothar 
Meyer. 

The first communication of Newlands, "On Relations 
among the Equivalents," appeared early in 1863.* 

In 1864 a list of the elements then known, was by him 
given in the order of their atomic masses the first list of the 
kind ever published. 

Mendeleeff first enunciated the periodic law in his work on 
chemistry, in 1869, and Lothar Meyer's announcement of it 
was made, independently, in the same year. 

The Periodic Law. The law is thus stated : The proper- 
ties of the elements are periodic functions of their atomic 
masses. 

A phenomenon is periodic when it recurs at definite inter- 
vals, while the conditioning circumstances vary continuously. 
In this case, the variable is the atomic mass, which increases 
constantly, while the properties of the elements recur at 
stated intervals. 

Although the dependence of all the physical and chemical 
properties of the elements upon their atomic mass, has not yet 
been clearly demonstrated, still, the numerous intimate rela- 
tions already firmly established, mark the Periodic Law as 
one of the most important laws of chemistry. 

As the manner of grouping the elements adopted by New- 
lands, Mendeleeff, and Lothar Meyer is not the same, although 
of course in each instance the elements are placed in the order 
of their atomic masses, all three arrangements are here given. 

Newlands' Table \ was first published in the Chemical 
Xeivs in 1875, where he stated : " Elements belonging to the 



* Chemical News, Vol. VII, p. 70, Feb. 7, 1863. 
f On the Discovery of the Periodic Law, and on Relations among the 
Atomic Weights. John A. R. Newlands. 



THE PERIODIC LAW. 



135 



same group stand to each other in a relation similar to that 
between the extremes of one or more octaves in music. Thus, 
if we commence counting at lithium, calling it 1, sodium will 
be 8 and potassium 15, and so on. To save the trouble of 
counting in each individual case, and also to render the rela- 
tionship obvious at a glance, it is convenient to adopt a hori- 
zontal arrangement/' 

Newlands' Table. 

Elements in Order of Atomic Weight. 

HORIZONTAL ARRANGEMENT. 



1. 


2. 


3. 


4. 


5. 


6. 


7. 


8. 


a 
b 
Q 


Li 7.0 
Be 9.4 
B 11.0 
C 12.0 
N 140 
O 16.0 
F 19.0 


Xa 23.0 
Mg 24.0 

Al 27.4 
Si 28.0 
P 31.0 
S 32.0 
Cl 35.5 


K 39.1 
Ca 40.0 




Cu 63.4 
Zu 65.2 


Rb 85.4 
Sr 87.6 
I 88.0? 
Zr 89.6 
Nb 94.0 
Mo 96.0 








Fe 56.0 




d 
e 
f. ... 
gHl. 


Ti 50.0 
V 51.2 
Or 52.2 
MD 55.0 




RU. 104.4 
Uu 104.4 
Pd 106.6 






As 75.0 
Se 79.4 
Br 80.0 


Ni58.8 
Co 58.8 






1. 


9. 10. 




11 


12. 


13. 


14. 


15' 16. 


a 
b 


Ag 108 
Cd 112 
In 113.4 
Sn 118.C 
Sb 122.C 
Te 128.C 
I* 127. C 


Cs 133.0 
Ba 137.0 
Di 138.0? 
>:Ce 140.0? 

I . 




Au 


197.0 










Hg 200.0 
Te 203.6 
Pb 207.0 
Bi 210.0 








;; 


Er 1780? 
La 180.0? 
Ta 182.0 
W 184.0 


pV 

Ir 
Os 


197'. 4 
198.0 
199.2 


d 
e 
f 

g 







Th 235.0 








::::::: 




.. 







U 240.0 



NOTE. " The quautivalence of the elements on the different hori- 
zontal lines is usually as follows : 
Line a, Monads. Line d, Tetrads. Line g, Monads (or 

" b, Dyads. " e, Triads (or Pentads). Heptads)." 

" c, Triads. " f, Dyads (or Hexads). 



?_F. G. W. 



136 



LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



Mendel6efFs Table* which shows the distribution of the 
elements in periods, shows two small periods, each containing 
seven elements, and five, so-called, large periods. 

The elements at the commencement of each series are base- 
forming, those at the end of the series are acid-forming 
elements. This is especially marked in the two short periods. 
The transition from base to acid forming elements is gradual, 
the intermediate members forming oxides, which are neither 
pronouncedly basic nor acid. 

There is a striking contrast in the chemical properties 
between the last member of any given series and the first 
member of the series next following. 

Mendeleeff's Table. 

The Atomic Weights of the Elements. 
DISTRIBUTION OF THE ELEMENTS IN PERIODS. 



Groups. 


Higher 
Salt- 
forming 
Oxides. 


Typical 
or 1st 
Small 
Period. 


Large Periods. 


1st. 


2d. 


3d. 


4th. 


5th. 


I.. 
II.. 
III.. 

IV.. 
V.. 
VI.. 
VII.. 

VIII 


R 2 

no 

R 2 3 
R0 2 
R 2 & 
R0 3 
R 2 7 
( 


Li = 7 
Be = 9 
B =11 
C =12 
N =14 
=16 
F =19 


K 39 
Ca 40 
Sc 44 
Ti 48 
V 51 
Or 52 
Mu 55 
Fe 56 
Co 58.5 
Ni 59 

Ou 63 
Zn 65 
Ga 70 

Ge 72 
As 75 
Se 79 
Br 80 


Rb 85 
Sr 87 
Y 89 
Zr 90 
Nb 94 
Mo 96 


Cs 133 
Ba 137 
La 138 
Ce 140 






| 


Ybl73 

Ta 182 
W 184 


Tli 232 





Ur 240 


Ru 103 
RU104 
Pdl06 

Agl08 
Cd 112 
In 113 
Sn 118 
Sb 120 
Te 125 
I 127 




Os 191 
Ir 193 
Pt 196 

Au 198 
Hg200 
Tl 204 
Pb 206 
Bi 208 




\" 








, I.. 

II.. 
III.. 

IV.. 
V.. 
VI.. 
I. VII.. 


( 






...... 


R 2 OJ 

RO 
R 2 3 
R0 2 
R a 6 
R0 3 
R 2 7 


H = i 
Na =23 
Mg = 24 

Al = 27 
Si =28 
P =31 
S =32 
01= 35.5 

IJdSmal? 
Period. 



































* The Principles of Chemistry, by D. Mendeleeff. Translated from 
the Russian (Fifth Edition) by George Kamensky and A. J. Greenaway. 
London and New York, 1891. 



THE PERIODIC LAW. 137 

Lothar Meyers Table* shows the symbols of the elements 
written in the order of their atomic masses, but in horizontal 
rows. 

Hydrogen being accepted as the unit of atomic mass, the 
first line is commenced by Li = 7.01, then comes Be = 9.08, 
and so on. Writing is continued in the same horizontal line 
until an element is reached, which resembles lithium in its 
chemical properties. 

The symbol of this element, Na = 23.0 is placed under 
that of Li, and thus forms the beginning of the second line, 
which line ends with Cl = 35.37. K = 39.03 begins the third 
line, and the writing is continued in this manner, until the 
symbols of all of the elements have been noted in the order 
of their atomic masses. 

If on the tabular scheme thus produced, horizontal lines 
be drawn under each line of symbols, and if vertical lines be 
drawn after each symbol, it will be seen, that the elements 
are divided into horizontal and into vertical rows. The 
former are termed series or periods, the latter, groups. The 
groups contain elements closely allied in their properties; for 
instance, Group I. consists of : Li, Xa, K, Kb, Cs. 

In the first two series, each of which consists of seven 
members, the two elements which fall into the same group, 
closely resemble each other; thus, for instance, Li and Na, C 
and Si, Fe and 01. 

The gaps which appear in all of these tables where they 
are indicated by dots will probably some day be filled by 
elements as yet undiscovered. 



* Outlines of Theoretical Chemistry, by Lothar Meyer. Translated 
by P. Phillips Bedson and W. Carleton Williams. London and New 
York, 1892. 



138 



LECTURE-NOTES ON THEORETICAL CHEMISTRY. 



Lothar Meyer's Table. 

Natural System of the Elements. 

HYDROGEN H = 1. 



I. 


n. 


III. 


IV. 


Li 7.01 
Na 23.0 
K 39.03 
Cu 63.18 
Rb 85.2 
Ag 107.66 
Cs 132.7 


Be 9.08 
Mg 24.3 
Ca 39.91 
Zn 65.10 
Sr 87.3 
Cd 111.7 
Ba 136.9 


B 10.9 
Al 27.04 
Sc 43.97 
Ga 69.9 
Y 88.9 
In 113.6 
La 138 
Yb 172 6 


C 11.97 
Si 28.3 
Ti 48.0 
Ge 72.3 
Zr 90.4 
Sn 118.8 
Ce 139.9 


i Au 196.7 


Hg 199.8 


Tl 203.7 


Pb 206.4 
Th 232.0 


V. 


VI. 


VII. 


VIII. 


N 14 01 


O 15 96 


F 19 06 




P 30 96 


S 31 98 


Cl 35 37 




V 51.1 
As 74.9 
Xb 93 7 


Cr 52.45 

Sc 78.87 
Mo 95 9 


Mu 54.8 
Br 79.76 


Fe 55.88 
Ru 101 4 


Sb 119 6 


Te 125 


I 126 54 












Ta 182 


W 183 6 




Os 191 


Bi 207 3 










U 239.6 






VI 


tl. 






















Co 58.6 


Ni 50.6 






Rh 102.7 


Pd 106.35 






Ir 192.3 


Pt 194.3 






::::::::: 









THE PERIODIC LAW. 139 

Atomic Analogues. Mendeleeff pointed out, that in many 
instances the value of any given property of an element is 
approximately the average of the values of the same property 
of the two elements which immediately adjoin it, either in 
the same series, or in the same group. 

Thus, glancing at Lothar Meyer's table, it will be seen that 
the atomic mass of S = 31.98 is approximately the mean of 
the atomic mass of P = 30.96 and 01 = 35.37 which adjoin 
it on the right and left, and that it is also the average of 
the atomic mass of = 15.96 and of Or = 52.45 which are 
placed immediately above and below it in the scheme. 

Four elements thus related, are termed atomic analogues. 

Similar groups of analogues can be traced with reference to 
other properties of the elements. 

Mendel6eff's Predictions. Mendeleeff, from such considera- 
tions, predicted the existence and the properties of elements 
which were to fill the gaps existing between boron and yttrium, 
aluminium and indium, and, silicon and tin, respectively. 
These elements received from him the provisional names of 
eka-boron, eka-aluminium, and eka-silicon. 

Gallium, discovered in 1875, proved to be the element 
whose existence and properties Mendeleeff had predicted as 
eka-aluminium; scandium, discovered in 1879, met the re- 
quirements claimed for eka-boron, and germanium, discovered 
in 1886, proved to have the atomic mass and the properties 
predicted for eka-silicon. 

Importance of the Periodic Law. A study of the elements 
when arranged in such systems according to the periodic law. 
has resulted not only in the prediction of the existence and 
the properties of elements as yet undiscovered, but has proved 
of value also in leading to the correction of several erroneous 
atomic mass values of some of the elements of tellurium, of 
caesium, and of indium, among others. 

Graphic Curved. Perhaps the best way of clearly bringing 
out the fact that the properties of the elements are periodic 



140 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

functions of their atomic masses, is to present these relations 
graphically, by means of curves. 

Such curves are of value in affording an immediate and 
comprehensive view over a great number of data, in illus- 
trating the co-ordination of different phenomena, and also 
in serving as a ready means for controlling the correctness of 
conclusions and inferences drawn from experiments. 

As was first shown by Lothar Meyer, the atomic volumes 
afford an excellent illustration of periodic variation. 

The term specific volume expresses the volume occupied by 
the unit mass of a substance; this value multiplied by the 
atomic mass of an element, gives as the product a value termed, 
the atomic volume. 

In the following cut the symbols of the elements are 
recorded on the horizontal line at distances from zero pro- 
portional to their atomic masses, and the atomic volumes are 
marked on the scale of the vertical line, according to their 
respective numerical value. 

The curves which result on combining the consecutive 
points are irregular, but bear a certain resemblance to each 
other. Taking the curve as a whole, it will be found to con- 
sist of two kinds of curves, or periods, as they are called. The 
first two are short, and the others are long periods. 

It will be seen, that the first element of each period is an 
alkali metal, and thus in general, similar positions in the dif- 
ferent periods are held by elements similar in their chemical 
properties. 



THE PERIODIC LAW. 



141 




142 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 

Periodicity of the Properties of Elements and Compounds. 

Many of the chemical and physical properties of the elements 
are periodic, and the same holds true of the properties of 
their compounds. 

Thus, the periodicity of valence, of the specific gravity in 
the solid state as shown by a comparison of the atomic vol- 
umes, of the electro-chemical properties, of the melting-point, 
of the magnetic power, of the refractive power, of the con- 
ductivity for heat and electricity, of the toxic properties of 
the metals, etc., have all been carefully studied. The period- 
icity of the molecular volume of the oxides, as well as the 
acid and the basic properties of these compounds, must also 
be mentioned. 

A tracing out of these different relations is most interest- 
ing, and although the periodic law cannot as yet give a logical 
explanation of all these phenomena, still it stands unques- 
tioned, that it is one of the most far-reaching, if it be not, 
the most important law of chemistry. 



SOLUTIONS. 143 



CHAPTER X. 
SOLUTIONS. 

Definition. Mixtures which are perfectly homogeneous, 
chemically as well as physically, and from which the com- 
ponents cannot be separated by mechanical means, are termed 
solutions. Sometimes they are also referred to as "physical 
mixtures," and this term is understood as embracing homo- 
geneous gaseous mixtures, solutions, alloys, etc. 
. The state of aggregation of substances determines to a 
great extent their ability to form solutions, and perhaps the 
best way to point out the relations obtaining, will be to consider 
briefly the behavior of substances towards each other when 
in the gaseous, the liquid, and the solid condition. 

Gases in Gases. Gaseous mixtures afford the best oppor- 
tunity for studying tjie behavior of solutions, because the 
existing conditions are most simple. 

If the gases are so chosen, that no chemical action takes 
place between them, the ability to form solutions is unre- 
stricted ; this means, that they can intermingle and mix with 
one another in all proportions. 

In such a mixture, each gas will retain to the fullest extent 
its original properties, and will exhibit the same in the 
same manner, as if it alone were present. 

Thus, the pressure exerted by any gaseous mixture is equal 
to the sum of the pressures exerted by its individual com- 
ponents. That is to say, each gas, uninfluenced by the 
presence of the other gases, exercises the same pressure which 
it would exercise if it alone filled the entire space, a fact 



144 LECTtJRE-HOTES OK THEORETICAL CHEMISTRY. 

already recognized by Dalton in 1802. This pressure is 
termed the partial pressure of the gas. 

The power of a gaseous mixture to absorb light and to re- 
fract light, has likewise been shown to be in accordance with 
the law of addition, in virtue of which, any given property of 
a gaseous mixture is equal to the sum of that property of its 
components. 

The reason why the laws governing solutions of gases in 
gases, are simple and easy of discernment, is found in the fact, 
that in the gaseous state the individual particles of matter 
are at a considerable mean distance from each other, a dis- 
tance sufficiently great to prevent the mutual action of the 
particles induced by close proximity. 

Gases in Liquids. With hardly an exception, all gases are 
soluble in all liquids, but the amount of different gases which 
liquids can dissolve, varies within very wide limits, and is de- 
pendent upon the nature of both the liquid and the gas 
concerned. 

The amount of a gas dissolved by a liquid is generally 
expressed in terms of volume, and not in parts by weight. 

" Coefficient of absorption " is the term used by Bunsen 
to denote the volume of a gas under standard conditions of 
temperature and pressure, absorbed by the unit volume of a 
given liquid under normal pressure. 

Ostwald uses the expression " solubility of a gas," to denote 
the ratio of the volume of gas absorbed to the volume of the 
absorbing liquid, at any specified temperature and pressure. 

Solutions of gases in liquids are divided into two groups: 

(a) Those solutions from which the dissolved gas can be 
removed easily by decreasing the pressure or by increasing 
the temperature; and (b) those solutions which refuse to yield 
up all of the dissolved gas when subjected to the indicated 
changes in pressure and temperature; but in such instances a 
chemical change has most likely taken place, thus leaving 
the matter no longer a problem of simple solution. 



SOLUTIONS. 145 

Solutions of gases in liquids, belonging to the first of these 
two groups, act in obedience to the law of Henry, which 
holds, that: the quantity of a gas dissolved by a certain 
amount of a liquid, is proportional to the pressure of the gas. 

Bearing in mind the fact that the volume of a gas is in- 
versely as the pressure to which it is subjected, Henry's law 
can also be thus stated: A given amount of a liquid will 
always dissolve the same volume of a gas, irrespective of the 
pressure. 

When a gaseous mixture is dissolved by a liquid, the quan- 
tity of each gas dissolved is proportional to its partial pressure; 
that is to say, in absorbing a gaseous mixture, the liquid ab- 
sorbs each constituent of this mixture as if it alone were 
present, and exerted its own independent pressure. 

Gases in Solids. A well-known instance of a gas dissolved 
in solids (metals), is furnished by the absorption of hydrogen 
by palladium, iron, platinum, potassium, and sodium. 

At a red heat, palladium will absorb about 935 times, 
platinum about 3.8 times, its own volume of hydrogen gas. 
Hydrogen has also been found absorbed " occluded," as it is 
termed, in certain meteorites. The meteorite of Lenarto, 
for instance, when heated in vacuo yielded more than 2.5 
times its own volume of this gas. 

Liquids in Gases. The tendency of liquids to pass into the 
gaseous condition, to evaporate, is closely allied to the facility 
with which liquids mingle with gases and form gaseous mix- 
tures. 

Dalton stated as the law obtaining in these cases: the 
vapor pressure of a liquid in a gas is the same as in a vacuum. 

The accuracy of this has been questioned by Regnault and 
others, but recently, careful observations made on the behavior 
of water and ether, in vacuo and in air, showed the differences 
to be very slight as a rule, not exceeding one per cent. 

Liquids in Liquids. In studying the solution of liquids in 
liquids, a division into three groups is generally made. 



146 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

GROUP I. embraces those liquids which readily mix with 
each other in all proportions; water and alcohol, for instance, 
will serve as an illustration of this type. 

But the solubility of liquids is materially affected by the 
temperature; and certain liquids for example, water and ani- 
line, which at the ordinary temperature will dissolve one 
another but very slightly will, if heated up to nearly 170, 
mix together in all proportions. Likewise, phenol and water 
become miscible in all proportions when a temperature of 80 
is reached. 

Generally speaking, the properties of mixtures of liquids 
are not additive, as was found to be the case in gaseous mix- 
tures. This means, that any given property of a mixture of 
liquids is not necessarily equal-to the sum of that property of 
its constituents. 

Thus, the volume of a mixture of two or more liquids is 
not necessarily equal to the sum of the volumes of the com- 
ponent liquids: in most instances it is smaller, than this 
sum. 

A satisfactory explanation of this has not yet been advanced ; 
for, although changes of temperature frequently occur on the 
mutual solution of liquids, such changes may consist in an 
increase or in a decrease of temperature, and no definite con- 
nection between changes in temperature and changes in the 
volume of the mixtures has yet been traced. 

GROUP II. consists of liquids which dissolve each other, but 
only in restricted proportions. 

An example of this type is afforded by water and ether. If 
a mixture of these two liquids is made, then, when separation 
into layers is brought about, the water solution will contain 
10$ of ether, and the layer of ether will be found to hold 3$ 
of water. 

GROUP III. is reserved for those liquids which exercise 
practically no solvent action on each other. There are even 
at present very few liquids which can be placed in this 



SOLUTIONS. 147 

group, and it seems likely, that improved methods of analysis, 
i.e., the power of determining very minute quantities of cer- 
tain substances, would transfer to the second group all liquids 
now classed in this division. 

Liquids in Solids. An instance of the solution of a liquid 
in solids is afforded by the mixture of mercury with the 
solid metals. Mixtures of this kind are termed amalgams. 
Amalgams may be solids they even frequently occur in the 
crystalline condition; or they may be liquids, in which case 
they contain a considerable excess of mercury. 

As a rule, amalgams are unstable, and some can be decom- 
posed by subjecting them merely to high pressure. 

The formation of amalgams is attended in some instances 
by the evolution, in others by the absorption, of heat. As to 
whether amalgams should be considered as chemical com- 
pounds or as physical mixtures, the preponderance of evidence 
seems to favor the latter view, although the existence of 
definite compounds of mercury with some metals is unques- 
tioned. 

Solids in Gases. Ostwald considers it justifiable to speak 
of the solution of solids in gases, " inasmuch as certain solids 
can be evaporated without going through the liquid condi- 
tion." * 

As yet the law of these phenomena has not been deter- 
mined by experiment, but Ostwald presumes that Dalton's 
law will be found to hold good also for solutions of solids in 
gases. 

Solids in Liquids. The solution of solids in liquids is the 
most common, as well as the most important instance of solu- 
tions to be considered. 

A solid soluble in a liquid will dissolve if it be merely left 
in contact with the solvent, but solution will in most cases be 



* Ostwald, W., Solutions, 1891 ; translated by M. M. Pattison Muir. 



148 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 

materially hastened if solid and solvent are well stirred or 
shaken together. 

When a solvent refuses to absorb any more of a solid, the 
solution is said to be saturated with respect to that solid. In 
other words, a solution is saturated, when at any given tem- 
perature the solvent has absorbed the maximum amount of a 
solid which it can normally hold in solution at that tempera- 
ture. 

Under certain conditions however, solutions can be made 
to contain more than the quantity above referred to, and in 
that case they are said to be supersaturated; but such super- 
saturated solutions can be formed by all soluble bodies, and 
this condition must not be considered as exceptional. 

The fundamental law governing the behavior of solids go- 
ing into solution in liquids, is analogous to that which is valid 
for vapor-pressures. 

The influence which pressure exerts on the solubility of 
substances has been much studied. 

Moller and Sorby demonstrated that a change of pressure 
affects the solubility independently of a change of tempera- 
ture. Recent investigations have shown, that although an 
increase of pressure generally conditions an increase of solu- 
bility, yet, at very high pressures a decrease of solubility is 
induced. 

The manner in which changes in temperature influence 
solubility was already examined into by Gay-Lussac in the 
first quarter of this century, and since that time this prob- 
lem has occupied the attention of several investigators. 

As a rule, solubility increases with increasing temperature, 
and usually the solubility increases faster than the tempera- 
ture increases. However, there are substances for instance, 
some of the salts of calcium the solubility of which is less 
at higher than at lower temperatures. 

When a solid is dissolved in a liquid, generally speaking, a 
diminution of volume occurs. The amount of this diminution 



SOLUTIONS. 149 

is determined by the ratio between the solvent and the solid 
dissolved; for a given amount of solid, the contraction is the 
greater, the greater the amount of solvent employed. 

Solids in Solids. Mixtures resulting from the permanent 
union of two or more metals which are solids at the ordinary 
temperature and pressure, are termed alloys. 

Alloys are usually prepared by the aid of heat, but some 
alloys, of certain soft metals, can be made by pressure alone, 
and without elevation of temperature. 

Whether alloys are true chemical compounds, or whether 
they are to be regarded as solutions of metals in each other, 
has long been a mooted question. 

Definite compounds of metals in definite proportions by 
weight, undoubtedly do exist. It is, however, difficult to 
isolate these compounds, as they seem to dissolve in all pro- 
portions in the melted metals; and, as a rule, it appears that 
alloys are mixtures of definite compounds with an excess of 
one or more metals. 

This view seems to be borne out by the fact that alloys pre- 
serve, more or less, some characteristics of their constituents. 

Solutions of solids in solids do not, however, necessarily ex- 
hibit an additive character in their properties. The melting- 
points are usually lowered, the average density is increased. 
In certain alloys the conducting power for electricity is pro- 
portional to the relative volume of the components; in other 
alloys this is not the case. In many instances the volume of 
an alloy is less than the sum of the volumes of its components; 
in other instances the reverse is true. 

Dilute Solutions. A condition analogous to that obtaining 
in the gaseous state, can be produced by causing a substance 
gaseous, liquid, or solid to enter into contact with a liquid 
solvent, with which solvent said substance will form a homo- 
geneous mixture, arranging the conditions so that the solvent 
will be present in considerable excess. 

Such a solution is termed dilute. It is evident that in such 



150 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

a solution the particles of the dissolved substance will be 
widely separated from one another, and the behavior of sub- 
stances when in a state of dilute solution, closely resembles 
the behavior of gaseous mixtures. 

When two solutions of the same substance, but of different 
concentrations, are placed in contact, the two solutions will 
mingle with each other, and their movement will continue 
until the composition of the entire solution is homogeneous. 

If this intermingling of the solutions is interfered with by 
the insertion of a membrane or of some other partition which 
will permit the passage of the solvent but not of the dissolved 
substance, then the latter will exert a pressure on the ob- 
structing partition. This pressure is spoken of as the osmotic 
pressure, and is undoubtedly produced by the dissolved sub- 
stance, for the" solvent can pass freely through the partition, 
and moreover, an increase in the amount of the dissolved 
substance is accompanied by a proportionate increase of press- 
ure on the partition. This power of movement is inherent in 
the particles of the dissolved substance, and it is merely ren- 
dered apparent by its action on the partition. 

The phenomena which are caused by the action of this 
force in the particles of dissolved substances are termed 
osmotic or pressure phenomena; the movements alluded to 
are spoken of as the phenomena of diffusion. Osmose and 
diffusion play a very important part in nature. 

Osmotic Pressure. The conditions which are of special 
importance in studying the gaseous condition are the volume, 
the temperature, and the tension under which gases exist. 

In dilute solutions, the first two conditions are determined 
by the volume and the temperature of the solvent, whereas, 
corresponding to the tension of gases, solutions exhibit the 
so-called osmotic pressure. 

As enunciated by Van't Hoff, this osmotic pressure is in- 
dependent of the nature of the solvent, and, in dilute solutions, 



SOLUTIONS. 151 

is subject to the laws obeyed by gases the laws of Boyle, 
Charles, and Avogadro. 

Thus, for instance, for constant volume, osmotic pressure is 
proportional to absolute temperature, and, for all gases and 
vapors which dissolve in a solvent in amounts proportionate 
to their pressure, the osmotic pressure is equal to the cor- 
responding gas-pressure. 

A careful consideration of most copious experimental data 
has led to the conclusion, that the osmotic pressure of a sub- 
stance in solution is equivalent to the gaseous pressure which 
would be observed, provided the solvent were removed and 
the dissolved substance, in the gaseous condition, were made 
to occupy the identical space. 

This fact is of great practical importance, because, as 
already explained in the chapter on the determination of 
molecular mass, it permits the molecular mass determination 
of substances, the vapor density of which cannot be ascer- 
tained. 

This peculiar relation between osmotic pressure and mo- 
lecular mass, obtained in a purely empirical manner, called 
for an explanatory hypothesis. 

Such an hypothesis was advanced by Van't Hoff, and it is 
practically an enlargement of Avogadro's Law, namely: 

Solutions of identical osmotic pressure, termed isosmotic or 
isotonic solutions, contain at a given temperature, in equal 
volume, the identical number of molecules of dissolved sub- 
stance ; moreover, this number of molecules is the same as 
would be contained in the identical volume of a perfect gas, 
at the same temperature and pressure. 

Measurement of Osmotic Pressure. Several methods have 
been devised for the direct measurement of osmotic pressure. 

Thus, Pfeffer placed a clay cell filled with a sugar solution, 
to which a little sulphate of copper had been added, into a 
dilute solution of ferrocyanide of potassium. This resulted 
in the deposition of a thin membrane of ferrocyanide of 



152 LECTURE-KOTES ON THEORETICAL CHEMISTRY. 

copper in the interior of the cell, a deposit which possesses 
the peculiarity of permitting water to pass through it, but 
which prevents the passage of many substances soluble in 
water, cane-sugar for instance. 

The sugar molecules are thus prevented from escaping, and 
if cell and contents are placed into a vessel with water, the 
latter, in obedience to the laws of diffusion, will permeate the 
membrane of ferrocyanide of copper, and, entering the cell, 
will increase the volume of the sugar solution. If the cell be 
provided with a mercury manometer, the osmotic pressure 
can be directly ascertained, or if, instead of having this at- 
tachment, a tube is inserted in the cell, the sugar solution 
will rise in this tube, and the height to which the solution 
will rise above the level of the liquid in the cell will serve 
as a measure of the intensity of the osmotic pressure of the 
solution. 

From Pfeffer's determinations many most interesting data 
were obtained. Thus, for instance, he found that the osmotic 
pressure is dependent to a very great extent on the nature of 
the dissolved substance; solutions of different substances of 
equal concentration produced very different, and some of them, 
very great pressures. For instance, a 1^ per cent solution of 
potassium nitrate produced a pressure of over three atmos- 
pheres. 

But in most cases, it is a matter of extreme difficulty to 
meiisare osmotic pressures directly, and various methods have 
been devised to obtain the result desired, in an indirect man- 
ner. 

All of these latter methods base upon a measurement of 
the amount of work which must be done in order to effect a 
separation of the solvent and the substance dissolved. For 
the osmotic pressure is a direct measure of this work, and 
therefore, if the latter be known, the former can be readily 
ascertained. 

Among the principal methods resorted to to effect this sepa- 



SOLUTIONS. 15o 

ration of the solvent and of the substance dissolved, crystalli- 
zation, evaporation, and selective solubility are perhaps most 
frequently employed. As each of these methods can be used 
in two ways, i.e., as either the solvent can be removed from 
the dissolved substance, or as the reverse can be effected, this 
practically opens up six distinct ways of indirectly determin- 
ing osmotic pressure. 

Diffusion. As has been previously stated, the power of 
movement is inherent in the particles of a dissolved substance. 
In virtue of this property when two liquids of unequal con- 
centration are placed in contact, they will mix with each other 
until a perfectly homogeiieous solution is produced. This 
process is termed diffusion, and is a manifestation of osmotic 
pressure. 

Graham, about the middle of this century, was the first to 
thoroughly investigate this matter, and in 1855 Fick ad- 
vanced the theory that, " the quantity of a salt which diffuses 
through a given area is proportional to the difference between 
the concentrations of two areas infinitely near one another." 
The truth of this statement was demonstrated by an inves- 
tigation made by H. F. Weber twenty-four years later. 

Graham, in his investigations, found that there is a very 
marked difference in the speed with which the particles of 
different substances move through water. To those substances 
which diffuse relatively fast and which generally occur in the 
crystalline form, he gave the name crystalloids, while those 
substances which diffuse slowly, and which usually are amor- 
phous, were by him termed colloids. 

Colloidal substances permit the passage of crystalloids, but 
are usually impervious to other colloids. 

By inserting a membrane of some colloid between pure 
water on the one hand and a mixture of colloids and crystal- 
loids on the other, a more or less perfect separation of the 
colloids and the crystalloids can be effected, because the 
latter will readily pass through the membrane and the colloids 



154 LECTURE-KOTES ON THEORETICAL CHEMISTRY. 

will not. The process of effecting a separation in this manner 
is termed dialysis parchment-paper is usually the substance 
used as a membrane. 

Even the brief outline sketch given in these pages of the 
laws of solutions and of the relations obtaining among them, 
will indicate the great importance which attaches to this 
department of theoretical chemistry ; it is undoubtedly along 
these lines that great advances will be made in the near 
future. 



ENERGY CHEMICAL AFFINITY. 155 



CHAPTER XL 
ENERGY CHEMICAL AFFINITY. 

Introductory. Associated with matter is energy, and, like 
matter, energy is indestructible. 

Energy is the cause of all changes, of all transformations in 
the universe, and is perhaps best defined as : the capacity of 
doing work, of overcoming resistance. 

Every particle of matter in space is in a determinate posi- 
tion with reference to other particles of matter. Continuous 
change of position is termed motion, and all energy is re- 
garded as primarily due to the motion of matter. 

Varying with the kind of motion, energy appears in various 
forms, as : heat, light, sound, as electrical, or as chemical 
energy. 

These forms of energy are to a great extent mutually con- 
vertible, and convertible without loss. 

Manifestations of energy are frequently referred to as 
forces, and as all energy is regarded as due to the motion of 
matter, force may be defined as : any cause that tends to pro- 
duce, change, or destroy motion. 

As energy is the cause of all change, many phenomena in 
nature are conventionally ascribed to the action of certain 
forces. Thus, the falling of bodies towards the surface of the 
earth is ascribed to the force of gravity; the combustion of a 
fuel, to the force of chemical affinity. 

Measurement of Force. In order to compare the magnitude 
of forces, it is necessary to effect their measurement, and in 
order that this may be done, some standard of measure, some 
unit of force must be adopted. 



156 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

Forces are equal when they can produce the same accelera- 
tion on the same mass or on equal masses, and therefore a 
force may be measured by comparing it with the gravity of 
some known mass of matter. 

THE GRAVITY UNIT OF FORCE is the gravity of any unit of 
mass, which unit of mass may of course be selected at pleasure. 

The attraction exerted by the earth upon a given mass is 
variable; it varies according to the position of the mass on 
the earth's surface with the latitude. Thus, at the sea-level, 
one gramme is drawn towards the earth with a velocity of : 

978.1 centimetres per second, if at the equator, 
980.6 " " " , " " latitude 45, 

983.1 " , " " the pole. 

The gravity unit of force is hence a variable value. 

THE ABSOLUTE UNIT OF FORCE is another unit by which 
force is measured. This unit represents the force that, acting 
during the unit of time on the unit of mass produces the unit 
of velocity. 

Different absolute units of force can be constructed, based 
on different units of time, length and mass. 

In science, the absolute or kinetic unit of force now almost 
universally adopted, is based, on the centimetre as the unit of 
length, on the gramme as the unit of mass, and on the second 
as the unit of time. This system of measurement is called 
the centimetre-gramme-second system, and is usually desig- 
nated as the 0. G. S. system. 

The absolute unit of force in the C. G. S. system, is called 
the dyne. The dyne is the force that, acting on a mass of 
one gramme for one second produces a velocity of one centi- 
metre per second. 

RELATION BETWEEN GRAVITY UNITS AND ABSOLUTE 
UNITS. Gravity units are easily transformed into absolute 
units. It has already been stated, that in latitude 45, one 
gramme is drawn to the earth with a velocity of 980.6 centi- 



ENERGY CHEMICAL AFFINITY. 157 

metres per second. A dyne has been defined as imparting a 
Telocity of one centimetre per second to a mass of one gramme, 
therefore, the weight of one gramme is equal to 980.6 dynes 
in latitude 45, at the sea-level. 

Measurement of Energy. Energy is measured by the work 
which it can accomplish. The units selected for such measure- 
ment are : 

a. The gravity unit. 

b. The absolute unit. 

THE GRAVITY UNIT OF WORK. The gravity-unit usually 
adopted, is the kilogramme-metre. It represents the work 
done in raising one kilogramme vertically through the height 
of one metre. 

THE ABSOLUTE UNIT OF WORK. The absolute unit of work 
and in consequence, of energy, adopted in science, is the erg. 

The erg represents the work done in moving a body, free to 
move, one centimetre against a force of one dyne. 

Thus, the work done in lifting one gramme one centimetre 
vertically against the force of gravity, in latitude 45, is equal 
to 980.6 ergs, for one gramme = 980.6 dynes in latitude 45. 
And again, in raising a body weighing 20 dynes vertically 
through a height of 50 centimetres 20 X 50, i.e. 1,000 ergs of 
work are done. 

The amount of kinetic energy possessed by matter depends 
upon the mass of this matter and upon its velocity. 

If, m denotes the mass. 

" v " " velocity with which m is moving, then.: 
Kinetic Energy %mv*. 

The answer obtained, is of course in terms of the erg. 

The Law of the Conservation of Energy states, that the 
sum of all the various energies in the universe is a constant 
quantity. 

The proof that matter is indestructible, can easily be given 
by quantitative chemical experiments, but the principle of the 
conservation of energy does not admit of such direct demon- 



158 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

stration. The truth of this law can however be readily 
proven by indirect evidence. 

For, if a law is true, then the prediction of certain results 
under certain conditions, must be possible, and in the case of 
this law of the conservation of energy, all tests ever made in 
this manner, have affirmed its correctness. Thus, for instance, 
Joule furnished the experimental demonstration of the law 
according to which work can be transformed into heat, prac- 
tically a proof of the law of the conservation of energy. 

Chemical Affinity. 

Introductory. The one manifestation of energy which is of 
the greatest importance in chemistry, is the force of chemical 
affinity. Attraction is one of the universal attributes of 
matter, but according to the conditions under which it is ex- 
ercised, for instance, whether at measurable or at inappreciable 
distances, whether between similar or between dissimilar par- 
ticles or masses of matter, its action is designated by various 
terms. 

Thus, gravitation or gravity is the name applied to attrac- 
tion when exerted at measurable distances; the particles or 
masses of matter between which it is exercised, may be similar 
or dissimilar. 

Attraction at inappreciable distances, when exerted between 
dissimilar particles is termed adhesion, between similar par- 
ticles, cohesion. 

An important point to be noted in this connection is, that 
the exercise of these various forms of attraction entails no 
change in the properties of the matter acted upon. 

When the various forms of matter come to be studied from 
the chemical point of view, it is found, that matter is endowed 
with a property, in virtue of which, two or more dissimilar 
particles when brought into intimate contact, can give rise to 
other forms of matter, the properties of which can be, and 
generally are, entirely different from their own. 



ENERGY CHEMICAL AFFINITY. 159 

For instance, when sodium, a metal, is, under proper con- 
ditions, brought into contact with chlorine, a poisonous gas, 
sodium chloride is formed, a white salt, which not only is 
non-poisonous, but which is actually essential to the animal 
economy. 

Again, when hydrochloric acid in aqueous solution, is 
allowed to act on calcium carbonate, a solid, there is formed, 
carbon dioxide, a gas, and chloride of calcium, a salt, both 
substances with properties entirely different from the proper- 
ties of the substances through the inter-action of which they 
were formed. 

This peculiar property of matter has been designated by 
various terms, viz. : affinity, chemical affinity, heterogeneous 
affinity, chemical attraction, chemical action, molecular gravi- 
tation, elective gravitation, and chemism. 

By exercise of chemical affinity, the physical, physiological 
and chemical properties of substances, either, or all, can be 
greatly influenced and affected. 

Chemical affinity can be modified by mechanical action, 
for instance, by pressure, agitation, or percussion. It can also 
be modified by the influence of light, by heat and by cold. 
Heat usually promotes, while cold exerts a retarding influence 
on chemical action. 

Hypotheses regarding the Nature of Chemical Affinity. 
Although nothing positive is known, even at the present day, 
concerning the nature of chemical affinity, yet a number of 
hypotheses concerning this subject have been advanced from 
time to time, and a brief review of these, in the order of their 
sequence, is not without interest. 

The Greek philosophers sought to explain the difference of be- 
havior between different substances, by assuming the existence 
of likes and dislikes, inherent in the various forms of matter. 

Under influence of the teachings of Galileo, these views of 
chemical affinity were abandoned, and chemical affinity came 
to be regarded as due to the actual bringing into use of little 



160 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

hooks, points and projections, with which the ultimate parti- 
cles of matter were conceived as endowed. 

The next important change of view in regard to the nature 
of chemical affinity, was due to Sir Isaac Newton. He ascribed 
chemical affinity to the attractive action of small particles, but 
held, that the cause of chemical actions differed from that of 
general gravitation in several ways, principally, with respect 
to the influence that distance exercised on the result. 

Bergman, Berthollet and others, deemed chemical affinity 
and gravitation to be forces of the same character, and claimed, 
that the seeming difference in their action must be ascribed 
solely to the difference in conditions under which these forces 
are exhibited. 

Sir Humphry Davy, as early as 1807, expressed the belief, 
that the primary cause of electrical and chemical effects 
might be the same force. Electrical phenomena resulted, 
when this force was exerted between masses of matter, 
whereas chemical phenomena appeared, when this force was 
exercised between the smallest particles of substances. 

A complete revolution in the ideas entertained with regard 
to the nature of chemical affinity, was introduced by Berzelius. 
Berzelius carefully studied the chemical effects produced 
by the electric current, and concluded electricity to be the pri- 
mary cause of activity in all Nature. He conceived each atom 
as bearing a charge of electricity both positive and negative; 
one of these charges predominated, and the dominant charge 
determined the electrical character of the atom. He regarded 
every compound as formed of two parts, one of which bore a 
charge of positive, the other of negative electricity. 

The work of Joule and Mayer about the middle of this 
century, demonstrated the relationship between chemical 
affinity and various forms of energy, such as heat, electricity, 
etc. The mutual transmutability of these forces was shown, 
and thus the necessity of any further theorizing as to the 
nature of chemical affinity no longer existed. 



EXERGY CHEMICAL AFFINITY. 1G1 

In other words, chemical affinity is now generally regarded 
as one of the manifestations of energy, and it seems certain 
that it can, at least partially, be transformed into heat, light 
and electricity. 

Measurement of Chemical Affinity. Attempts to measure 
chemical affinity have been numerous and varied. 

Laplace studied the action of acids upon compounds decom- 
posable by acids, and expressed the view, that the intensity of the 
action of an acid was directly proportionate to its specific gravity. 

Morveau, Gay-Lussac and others, believing, that adhesion 
must be regarded as the first stage of chemical affinity, by 
means of weights determined the force necessary to separate 
disks of uniform size, from various liquids. These disks were 
constructed of different materials, for instance, of metal, of 
glass, etc. 

Wenzel, who commenced his investigations of the laws of 
chemical affinity in 1777, believed that the times required for 
the solution of metals in weak acids, afforded a means of meas- 
uring the strength of chemical affinity. 

The fact, that different amounts of heat are required to 
effect the decomposition of different compounds, led Lavoisier 
and others to attempt a measurement of chemical affinity on 
this basis. For instance, it was noticed that FeS., is decom- 
posed by a temperature of 816 C. and that sulphur volatilizes 
at 447 C.; the difference between these two values, was pro- 
nounced to be the numerical expression of the affinity between 
iron and sulphur. 

This idea, advanced thus early in the history of chemical 
theory, may be regarded as the foreshadowing of a hypothesis 
concerning the nature of chemical affinity, which was brought 
forward at a much later date. This hypothesis holds, that 
chemical affinity consists in an attraction between the atoms, 
and that this attraction is dependent on variations in the 
potential energies of the atoms. 

The thermal changes which accompany chemical reactions, 



162 LECTURE-NOTES Otf THEORETICAL CHEMISTRY. 

have been regarded as indicative of the transformation of 
potential energy into kinetic energy, and attempts have been 
made to measure this transformation of energy by thermal 
methods. But thermal measurements, although they serve to 
throw some light on certain phases of the question, cannot 
lead to an understanding of the nature of chemical affinity, 
because the values yielded by the present methods of thermo- 
chemistry, express but the ultimate outcome of several chemi- 
cal changes, the sum or the difference between the heats of 
decomposition and the heats of formation of the factors 
involved. Moreover, a portion only of chemical energy is 
transformed into heat, while other portions may appear in 
different forms. Von Helmholtz designates the former por- 
tion as bound, the latter, as free energy. 

The theory, that the force acting between two different 
kinds of matter is analogous to the force acting between two 
masses of matter, had, in its day, a number of eminent men 
among its adherents. Reactions occurring between com- 
pounds, involving both decompositions and combinations, 
were ascribed to the action of two opposite forces, in which 
the stronger chemical affinity gained the victory. 

This view found expression in the so-called "Tables of 
Affinity." In these, substances were arranged in the order of 
their supposed affinity for one another. 

The earliest of these tables, of which the following is a 
specimen, were published by H. Geoffroy in 1718. 

Table of Attraction. 

SULPHURIC ACID. POTASH. 

Baryta , Sulphuric acid 

Strontia Nitric acid 

Potash Muriatic acid 

Soda Acetic acid 

Lime Carbonic acid 
Ammonia 
Magnesia 



ENERGY CHEMICAL AFFINITY. 163 

Bergman, in recognition of the fact, that chemical reactions 
vary according to the conditions under which they take place, 
in his tables of affinity, stated the behavior of each substance, 
when in aqueous solution, "in the wet way," and when at the 
temperature of fusion, "in the dry way." The following for 
instance, is the table he formulated for potash. 

POTASH. 

Wet Way. Dry Way. 

Sulphuric acid Phosphoric acid 

Nitric " Boric " 

Hydrochloric " Arsenic " 

Phosphoric " Sulphuric " 

Arsenic " Nitric " 

Acetic " etc. Hydrochloric " etc. 

Kirwan sought a solution of the problem in the different 
percentage amounts of the constituents of salts, i.e. of acids 
and bases. He formulated two general laws based on his 
observations. " The quantity of any base required to saturate 
a given quantity of any acid is directly as the affinities." 
And, "The quantity of any acid required to saturate any 
given quantity of a base, is inversely as the affinities." 

Bethollet, whose views on chemical affinity have already 
been referred to, was the first to emphasize the important 
influence which is exercised by the quantity of the various 
factors taking part in any chemical reaction. Whether a 
certain metathesis takes place or not, depends not only on the 
so-called affinity, which the different factors may have for 
one another, but also on the relative amounts in which these 
factors are present. 

To elucidate this particular aspect of the question, was the 
aim of the researches of two Norwegian scientists Guldberg 
and Waage, who enunciated a mathematical law with respect 
to the influence of mass. 

They claimed, that the amount of a chemical change is 



164 LECTURE-KOTES OK THEORETICAL CHEMISTRY. 

proportional to the products of the active masses of the 
bodies concerned, and the coefficients of affinity of the reac- 
tion, of course presupposing elimination of secondary actions. 

The term " coefficient of affinity " is best explained in their 
own words.* " In a simple decomposition of the form AB -\- 
C AC-}- B, the formation of AC is chiefly brought about 
by the attraction between A and C; but there are also attrac- 
tions between the other substances, and ihe force which causes 
the formation of AC is the resultant of all these attractions. 
This force may be regarded as constant for a definite temper- 
ature; we represent its amount by k, which we call the coeffi- 
cient of affinity for the reaction in question. 

In the same way, in the double decomposition, AB -f- CD = 
AC -f- BD, the force which causes the formation of the new 
substances, is a function of all the attractions between the 
bodies A, B, C, D, AB, CD, AC, and BD, and the resultant 
force, k, is the coefficient of affinity for the reaction." 

Among other investigators whose labors have been directed 
to studying the influence of mass in chemical reactions, there 
should be mentioned H. Rose, Bunsen, Debus, Gladstone, and 
Ostwald. 

The theory of Guldberg and Waage, which later on was 
formulated as a law by Van't Hoif, is practically identical 
with the views of Williamson and Pfaundler. L. Pfaundler, 
in 1867, was the first who applied hypotheses resting on a 
mathematical basis, to the views concerning the states of ag- 
gregation of matter, which had been advanced by Bernoulli, 
Joule and others. 

Later on this theory was developed principally by Clausius 
and Maxwell, who assumed that substances consist of mole- 
cules, which are in continuous motion. It is claimed, that in 
the gaseous state, the velocity of the motion is directly pro- 
portional to the temperature, and inversely proportional to the 

* From M. M. P. Muir : A Treatise on the Principles of Chemistry. 



ENERGY CHEMICAL AFFINITY. 165 

square root of the molecular mass. There is supposed to be 
an oscillatory motion within the molecules, which in its in- 
tensity, stands in a definite relation to the motion of the mole- 
cules themselves. These views lend themselves readily to an 
explanation of partial reactions, of reversible reactions, and so 
forth. 

The study and the measurement of chemical affinity by 
electrical methods has engaged the attention of many of the 
most eminent investigators, among them, of Faraday, Sir W. 
Thomson, Von Helmholtz and Ostwald. 

The view is held, that in all solutions capable of conducting 
an electric current, the ions do not owe their existence to the 
action of the electric current, but that they exist as such, 
before the passage of the electrical current. 

The electric conductivity of solutions is thus made to serve 
as a means for ascertaining the condition of the substances 
which are dissolved, for the number of dissociated molecules, 
i.e. the ions, determine, and are therefore a measure of, the 
quantity of electricity passing through a solution. The 
term "conductivity" represents the quantity of electricity 
which is conveyed in unit time by unit electromotive force. 

The conductivity possessed by a solution which contains 
the molecular mass in grammes, of the electrolyte, is termed 
the molecular conductivity. This molecular conductivity in- 
creases with the temperature, and with the degree of dilution. 

The conductivity of equivalent quantities, is called equiva- 
lent conductivity. As all equivalent ions transport the same 
quantity of electricity, and as the amount of electricity 
transported in a given time and by a given electromotive 
force, is directly proportionate to the number of moving ions 
and to the speed with which they move, to quote the words 
of Ostwald, "the equivalent conductivity is thus a direct 
measure of the velocity of migration of the ions." 

As first enunciated by KohJrausch, the molecular conduc- 



166 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

tivity of an electrolyte is equal to the sum of the velocities of 
migration of the ions, or if : 

m = molecular conductivity, 
a = velocity of migration of anion, 
c = velocity of migration of cathion, 
x = the amount of the electrolyte dissociated into ions, 

then, 

m= x(a -\-c) 

As can be shown by experiment, it is only on attaining 
infinite dilution, that the dissociation of an electrolyte into its 
ions becomes complete, and then : 

m GO = a -f c 
From these equations, 

m= x(a + c) 

m oo = a -\- c 

by division, there is found, 

m 

Ju 

m co 

This formula expresses the fact that, " the degree of dis- 
sociation of a dissolved electrolyte at any state of dilution is 
equal to the ratio of the molecular conductivity at this state, 
to the molecular conductivity at infinite dilution," and this 
value x, is made to serve as a measure of the chemical affinity 
of substances. 



THERMAL RELATIONSTHERMOCHEMISTRY. 167 



CHAPTER XII. 
THERMAL RELATIONS-THERMOCHEMISTRY. 

Introductory. According to the theory of undulation, now 
generally accepted, heat is caused by the oscillatory motion 
of molecules. It is a form of energy, and is supposed to be 
transmitted through the intervention of an imponderable 
medium termed ether, which is assumed to completely pervade 
all space, that between molecules included. 

Temperature. The term temperature is given to that por- 
tion of heat, which can be perceived by the senses. 

Variations in temperature are appreciable to the sense of 
touch; the extremes of the sensations experienced, are termed 
heat and cold. The sense of touch furnishes, however, only 
a relative indication of the temperature of a body, that is to 
say, through this sense of touch it can only be determined 
whether a substance is more warm or less warm than some 
other substance. 

To ascertain the temperature of a body, resort is had to the 
physical action of heat on substances. As a rule, the expan- 
sion of substances caused by heat is measured and the value 
found is expressed in terms of some arbitrary unit. 

Temperatures from about 40 to about -f- 340 C. are 
usually registered by means of thermometers. The medium 
selected for use in thermometers is generally mercury, because 
this metal expands quite uniformly throughout the range 
indicated. Very high temperatures are measured by various 
devices. Sometimes they are determined by measuring the 
expansion of gases; rings made of different metals and alloys, 



168 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

or cones constructed of fire-clay, the fusing points of which 
are known, are frequently made use of for the purpose. 

Although temperature must not be confounded with quan- 
tity of heat, yet temperature can be made to serve as a basis for 
the measurement of heat quantity, because it always requires 
the same amount of heat to raise the temperature of a given 
amount of a substance from one determined point to another. 

Heat Units. In. order to measure amounts of heat, some 
thermal unit has to be selected in terms of which the values 
found, can be expressed. 

The unit of heat adopted, is the amount of heat necessary 
to raise a unit mass of pure water through one degree of a 
thermometer-scale. Different values are in use, varying with 
the units of weight and with the thermometer-scale employed. 

The unit of heat now generally accepted, is the amount of 
heat required to raise the temperature of 1 kilogramme of 
pure water from to 1 C. For some purposes, the amount 
of heat required to raise the temperature of 1 gramme of 
water from to 1 C. is adopted as unit. In these pages 
the term kilogramme-calorie (k. c.) will be used to denote the 
former, and the term gramme-calorie (g. c.) to designate the 
latter value. 

The temperature of the water chosen as the standard tem- 
perature, is sometimes 4 C., sometimes, some other tempera- 
ture more convenient for the purposes of the work undertaken, 
but, whatever the value taken, according to this method, a 
quantity of heat is measured by the quantity of water at a 
selected temperature which that quantity of heat would raise 
one degree in temperature. 

Mechanical Equivalent of Heat. The mechanical equivalent 
of heat is 423.99 kilogramme-metres. This means, that the 
energy, in form of heat, which is required to raise the temper- 
ature of one kilogramme of water from to 1 C. can perform 
work equivalent to raising the weight of 1 kilogramme through 
a height of 423.99 metres. 



THERMAL RELATIONS THERMOCHEMISTRY. 169 

Latent Heat. When matter is caused to pass from the 
solid to the liquid state, or, from the liquid to the gaseous 
state, a certain amount of heat is absorbed, which is not indi- 
cated by the thermometer. This heat is called latent heat, 
and it may be defined as: The amount of heat required to 
effect a change of state of a body without affecting its tem- 
perature. 

The latent heat of liquefaction is the amount of heat 
necessary to convert a substance from the solid into the liquid 
state, without sensibly affecting the thermometer. Thus, the 
latent heat of water is between 79 and 80, i.e., it will require 
between 79 and 80 heat-units to convert 1 kilogramme of ice 
at C. into water at C. In reversing the process, i.e. con- 
verting the water again into ice, the above-mentioned number 
of heat-units are again set free. 

The latent heat of vaporization is the amount of heat 
necessary to convert a substance from the liquid to the gase- 
ous state, without sensibly affecting the thermometer. Thus, 
the latent heat of steam is 537. This means, that 1 kilo- 
gramme of water at 100 C. absorbs 537 heat-units in its 
transformation into steam exhibiting a temperature of 100 C. 
In condensing steam into water, all of the heat-units previ- 
ously absorbed are again yielded. 

Specific Heat. The specific heat of a body, previously re- 
ferred to in connection with the determination of atomic 
masses, is the ratio of the amount of heat required to raise a 
given weight of a body one degree in temperature, compared 
to the amount of heat required to raise the same weight of 
water, one degree in temperature. 

Determination of Specific Heat. In the determination of 
specific heat values, three methods are principally used. 

These are : 

1. The method of the ice calorimeter. 

2. The method of mixtures. 

3. The time method. 



170 LECTURE-NOTES Otf THEORETICAL CHEMISTRY. 

1. THE METHOD OF THE ICE CALORIMETER. In this 
method, a known weight or the substance is heated to a cer- 
tain temperature. This temperature is noted, and then the 
substance is surrounded by dry ice at C., and allowed to 
remain in contact with this ice until the temperature of the 
substance has fallen to C. The amount of water formed 
by the partial melting of the ice is weighed, and the calcula- 
tion is based on the latent heat of liquefaction of ice. 

Of course proper precautions must be taken in all such 
experiments, to avoid as much as possible loss of heat by ra- 
diation, conduction, etc., so that all the heat lost by the sub- 
stance may be considered to have been absorbed by the ice. In 
these experiments the data required, are : 

1 . Weight of the substance. 

2. Initial temperature of the substance. 

3. Weight of the water formed. 
The substance will have lost : 

(1) X (2) X specific heat 
The water will have gained : 

(3) X 79.25* 

Since, according to the conditions of the experiment, all 
that has been gained in heat by the one substance has been 
lost by the other, these two quantities must be equal to each 
other, and as a result, we have an algebraic equation in which 
the specific heat sought is the only unknown quantity. 

EXAMPLE: Weight of a mass of nickel ............... 145.9 gms. 

luitial temperature of tbe nickel ........... 500 C. 

Weight of water formed .................. 100 gms. 

The nickel has therefore yielded in heat-units 0.1459 X 500 X specific 
heat of Ni., and the ice has absorbed, in heat-units: 0.100x79.25. 
Therefore, 

0.1459 X 500 X specific heat of Ni = 0.100 X 79.25 

7 Q95 
Specific heat of nickel = ~^i = 0.10863. 



Accepting this as the latent heat of water. 



THERMAL RELATIONS THERMOCHEMISTRY. 171 

2. THE METHOD OF MIXTURES. A known weight of the 
body whose specific heat is to be determined, is mixed with a 
known weight of water or of some other substance, the spe- 
cific heat of which is known. The temperatures of the two 
components are noted at the moment of mixture, and the 
temperature of the mixture is taken after thermal equilibrium 
has been established, that is, when both components have 
attained the same temperature. The necessary data are : 

1. \Veight of the substance, the specific heat of which is to 
be determined. 

2. Temperature of this substance before mixture. 

3. Weight of the substance, the specific heat of which is 
known. 

4. Specific heat of this substance. 

5. Temperature of this substance before mixture. 

6. Temperature of the mixture. 

The difference between (6) and (5) gives the change in 
temperature of the substance whose specific heat is known; 
the difference between (G) and (2) is the change experienced 
by the substance experimented on. Having obtained these 
values, the rest of the calculation is made as in the preceding 
instance. 

This method is used principally to determine the specific 
heat of liquids, but it can also be employed to determine the 
specific heat of solids, as shown in the following example. 

EXAMPLE : Weight of a piece of zinc 2 kilogrammes. 

Initial temperature of the zinc 150 C. 

Weight of water used 3 kilogrammes. 

Specific heat of water 1. 

Initial temperature of the water 10 C. 

Final temperature of the mixture 18.4 C. 

The zinc has lost : 

2 X (150-18.4) X specific heat of Zn. 



172 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 
The water has gained : 

3 X (18.4-10) X 1. 
Therefore, 

25 2 

Specific heat of zinc = - = 0.0957. 



The ice calorimeter may evidently be regarded as a special 
application of the method of mixtures. 

3. THE TIME METHOD. In this method, sometimes termed, 
the method of cooling, a known weight of the substance, the 
specific heat of which is to be determined, is heated to a cer- 
tain temperature, and then allowed to cool. The time which 
it needs to cool down to a certain temperature, compared with 
the time required, under identical conditions, by a known 
weight of water, or some other substance of known specific 
heat, to cool to the same extent, is made the basis of the cal- 
culation; the times for identical weights being proportional 
to the specific heats. 

The data required, are: 

1. Weight of the substance a, the specific heat of which is 
to be determined. 

2. Time in which this substance a, cools a stated number of 
degrees. 

3. Weight of the substance b, the specific heat of which 
is known. 

4. Specific heat of this substance b. 

5. Time in which this substance b, cools to the same extent 
as a. 

In making determinations by this method, equal volumes 
of the substances are taken, which differ in weight by amounts 
proportional to their respective specific gravities. 

The method of calculation used in this method, is best 
illustrated by a problem. 



THERMAL RELATIONS THERMOCHEMISTRY. 173 

EXAMPLE : Determine the specific heat of turpentine. 
Weight of turpentine ....................... = 1.3 kilogrammes. 

Time in which 1.3 kilogrammes of turpen- 

tine will cool from 25 to 5 C ............ 22 minutes, 9 seconds. 

Weight of water ........................... = 1.5 kilogrammes. 

Specific heat of water ...................... =1.0. 

Time in which 1.5 kilogrammes of water will 

cool from 25 to 5 C ..................... =60 minutes. 

1.5 : 60 : : 1.3 : 



That is to say, y = 52 minutes. This is the time required for 1.3 kilo- 
grammes of water to cool from 25 to 5 C. Hence : 

Time for cooling of 1.3 kilogrammes of water : Time for cooling 1.3 
kilogrammes of turpentine : : Sp. lit. of water : Sp. ht. of turpentine. 

52 : 22.15 : : 1 : x 

x = 0.426 
Therefore, the specific heat of turpentine = 0.426. 

Of course, if in place of water, any other substance is used, 
the specific heat of which is known, the corresponding values 
for this substance must be used in place of those given for 
water in the above example. 

This method is the least accurate of the three here de- 
scribed, but is convenient of application in certain instances. 

The specific heat of gases may be determined either under 
constant pressure, or under constant volume. The tables of 
these data usually bring the former values, unless the contrary 
is specified. 

Combustion. In the process of combustion, the energy 
which is liberated in the formation of the products of com- 
bustion, appears principally as heat. In instances of the 
perfect combustion of the ordinary fuels, these products are 
carbon dioxide and water. 

CALORIFIC POWER. The calorific power of a substance is 
the amount of heat, i.e. the number of heat-units, evolved by 



174 LECTURE-NOTES OK" THEORETICAL CHEMISTRY. 

the combustion of one unit-weight of the substance. The 
gramme or the kilogramme is usually the unit weight selected. 
CALORIFIC INTENSITY. The calorific intensity is the max- 
imum theoretical temperature to which the products of com- 
bustion are raised. 

The calorific power of a substance is a constant value. It 
is immaterial whether the combustion proceeds rapidly or 
slowly, whether it is completed at once, or is achieved in 
several stages. 

Calorific intensity however, is a value dependent, to a 
certain extent, on the conditions under which the combustion 
is effected. 
Let: 

C. J. represent the calorific intensity, 
C. P. represent the calorific power, 
8, S', 8", represent the specific heats of the products 
of combustion of one unit weight of the 
substance, 

m, m', m", represent the amounts by weight of the 
products of combustion of one unit weight 
of the substance. 

Then: 



In this formula there are reckoned as the products of com- 
bustion, not only the carbon dioxide and the water produced, 
but also the nitrogen of the atmosphere if the combustion 
takes place in air, and the mineral matter, the ash of the fuel, 
if it contains any, for heat is used in raising the temperature 
of these bodies. 

If water is produced in any process of combustion, atten- 
tion must be paid to the state, liquid or gaseous, in which it 
is obtained. 

The calorific power of 1 kilogramme of hydrogen burned 



THERMAL RELATIONS THERMOCHEMISTRY. 175 

in oxygen is 34,462 kilogramme-calories. This value includes 
the latent heat given out on the condensation of the water- 
vapor to the liquid state, that is, during its change from steam 
at 100 0. to water at 100 C. 

In ordinary combustions, the water remains in the gaseous 
state, therefore, if the calorific intensity of hydrogen is to be 
calculated from its calorific power, there must be deducted 
from the value above given, the latent heat of vaporization 
of the water formed. 

EXAMPLES. 
Calculation of Calorific Power. 

The symbol of methyl alcohol is CH 3 OH. It is required to calculate 
its calorific power. 

The first step is the calculation of the percentage composition of the 
substance named. 

C = 12 12 * 10 = 37.50 per cent. 
o2 

H.= 4 4 -^ =12.50 " 

1 \x inn 
O = 16 



32 
32 100.00 

As the calorific power of combustibles is usually given for 1 kilo- 
gramme of the substance, the composition of methyl alcohol i? 
expressed in parts per thousand, and is, 

C= 375 
H= 125 

O = 500 
1000 

It is customary to assume all of the oxygen present in a combustible 
to be combined with hydrogen, and the first calculation made, is to 



KG LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

ascertain how much of the hydrogen present is thus in combination 
with the oxygen in the form of water.* 

O :2H :: 500 : x 
16 : 2 : : 500 : x 
x = 62.50 

Total amount of H present ..................... = 125.0 

H in combination with O ...................... = 62.5 

H available as fuel ............................ = 62.5 

The calorific power of 1000 grammes of carbon = 8080 heat-units, 
(k. c.) 

Calorific power of 1000 grammes of hydrogen = 34,462 heat-units, 
(k. c.) 

Therefore, the carbon present, 375 grammes, yield : 

= 3030 heat-units, k. c. 



and the hydrogen present, available as fuel, 62.5 grammes, yield : 

34,462X62.5 

- = 2154 heat-units, k. c. 
1000 

3030 
2154 

Total, 5184 heat-units, k. c. 
There must now be determined the total amount of water produced 

2H : H 2 O : : 125 : x 
2 : 18 :: 125 : x 
y = 1125 

This means, that 1125 grammes of H 2 O are formed. 



* If there is not enough hydrogen to satisfy all of the oxygen, then a 
certain amount of the carbon is assumed to exist in combination with 
the oxygen, and only the balance of the carbon present is calculated as 
available for thermic effect. 



THERMAL RELATIONS THERMOCHEMISTRY. 17? 

1000 grammes of water absorb 537 heat units in passing into the 
gaseous condition, 1125 grammes absorb 604 beat units, (k. c.) for : 

1000 : 1125 :: 537 : x 
x = 604 

Heat-units produced, (total) .......... ........ 5184 k. c. 

Heat-units absorbed ............... .......... 604 ' ' 

Calorific power of CH S OH ................ = 4580 k. c. 

Calculation of Calorific Intensity. 

Calculate the calorific intensity of ethyl alcohol, burned in oxygen. 

The calorific power of ethyl alcohol 

(1 kilogramme) .................... = 6850 kilogramme-calories. 

Specific heat of steam ......... ......... = 0.475 

Specific heat of carbon dioxide .......... = 0.2164 

The combustion of ethyl alcohol takes place according to the equation : 

C 2 H 6 -f 30, = 2C0 2 + 3H a O 
On the combustion of 1 kilogramme of C a H 6 OH, there are formed : 

C a H 6 OH:2C0 2 :: 1 : * 

46 : 88 :: 1 :x 

x = 1.913 kgs. CO,. 

And: 

C 2 H 5 OH : 3H 2 :: 1 : x 

46 : 54 : : 1 : x 

x= 1.227 kgs. H 2 O 

The calorific intensity is calculated by application of the formula 
previously given : 

P T _ 

~ 



1.913 X .2164 + 1.227 X -475 

6850 _ 6850 
~ :4l39-f.5828 ~ .9967 

and the calorific intensity, of ethyl alcohol = 6872 C. 



178 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

Thermochemistry. 

Of all the forms in which energy is manifested, there is 
perhaps none of greater importance, and of more frequent 
occurrence, than that denoted as chemical energy. But not- 
withstanding this fact, unfortunately, no means are known 
whereby energy, appearing in this form, can be directly meas- 
ured. 

Chemical energy is however readily transformed into heat, 
and thermochemistry has for its object the measurement of 
chemical energy in thermal units ; the amount of heat liber- 
ated or absorbed in chemical processes, serving as a measure 
of the changes taking place in the chemical energy of the 
system or systems, involved in a given operation. 

Methods Employed in Thermochemistry. The apparatus 
used to make thermochemical determinations of course varies 
considerably, according to the nature of the determination to 
be made. Measurements which are to be made on substances 
in aqueous solutions, are conducted in a vessel termed a calo- 
rimeter ; these calorimeters are generally made of glass or of 
platinum. 

If of metal, the sides of the calorimeter are made as thin as 
possible. Its capacity generally ranges from about five hun- 
dred to one thousand cubic centimetres ; its shape is usually 
cylindrical. This cylinder is provided with a very accurate 
thermometer, graduated in fiftieths of a degree. This allows 
readings to be made accurately to yj-j- of a degree, and, when 
read by a telescope, permits estimations up to -^^ of a degree. 
Insulation of this cylinder is made as perfect as possible, in 
order to prevent loss of heat by radiation. 

The experiments made, are completed in as short a time as 
possible ; the actual rise in temperature of the water is never 
allowed to exceed a few degrees, and great care is taken to 
distribute the heat generated uniformly through the water, by 
means of mechanical stirrers, which are kept constantly in 
motion during the progress of the experiment. 



THERMAL RELATIONS THERMOCHEMISTRY. 179 

Of course, the weight of all parts of the apparatus, as 
well as that of the water, must be very carefully ascertained. 
Furthermore, allowance must he made for the specific heat 
of the metal, of which the apparatus is constructed. 

If, for instance, the vessel is made of platinum, which has a 
specific heat of 0.032, and if it has a weight of 180.0 grammes, 
then : 

180.0 X 0.032 = 5.760, 

which amount must be added to the weight of the water con- 
tained in the calorimeter, for this weight of platinum is equiv- 
alent to, i.e., has the same calorific value, as 5.760 grammes 
of water. 

Lavoisier was probably the first one to'study thermo-chem- 
ical phenomena from a theoretical point of view ; he recog- 
nized the principle, that, in the formation of a compound 
from its elements, the same amount of heat is set free as 
is required to decompose this compound. In 1840, G. H. Hess 
announced the important law of constant heat-summation, 
viz. : " the initial and final stages alone determine the develop- 
ment of heat in chemical processes." 

Laws of Thermochemistry. The following are the three 
fundamental laws of thermochemistry as formulated by Ber- 
thelot : 

I. The amount of heat set free in any chemical reaction is 
a measure of the total work, both chemical and physical, ac- 
complished in the reaction. 

II. Whenever a system of bodies undergoes physical or 
chemical changes capable of bringing it to a new state, with- 
out producing any mechanical effect exterior to the system, 
the amount of heat set free or absorbed in these changes, 
depends only on the initial and final states of the system, and 
is independent of the nature or order of the intermediate 
states. 

III. Every chemical change which is effected in a system 



180 LECTURE-^OTES 0^ THEORETICAL CHEMISTRY. 

without the aid of outside energy, tends to the production of 
that body or system of bodies, the formation of which, evolves 
the maximum heat. 

These principles permit the determination of thermal val- 
ues of reactions, which cannot be directly measured. 

In 1853, Julius Thomsen first applied the results of the 
mechanical theory of heat, to thermo-chemistry. 

The principal work thus far done in thermochemistry, has 
resulted in the accumulation of a very great number of obser- 
vations concerning the heat of formation of substances.* 

In making these determinations on the heat of formation of 
compounds, the molecules of the elements have been chosen as 
the starting point. However, as for the most part the mole- 
cules of elements are combinations of atoms, and as in the 
formation of molecules from these atoms chemical energy must 
have come into play, the problem of ascertaining the heat of 
formation of compounds is not a simple one. 

For, before the molecules of compounds can be formed, the 
atoms which make up the molecules of the elements engaged 
in the reaction, must be separated from one another. This 
requires energy, and therefore the heat of formation of a com- 
pound merely expresses the difference in energy (heat), between 
the amount required to separate the atoms of the elementary 
molecules, and the amount of energy (heat) evolved or absorbed 
in the formation of the new compound. 

If the latter value is greater than the former, and this is 
generally the case, the heat of formation of a compound is 
a plus (-J-) value; if the energy (heat), evolved on the forma- 
tion of a compound is less than the energy required to separate 
the atoms of the original molecules, then the heat of forma- 
tion of that compound is a minus ( ) value. 

* For tables of these data see the " Annuaire," published by the Bu- 
reau des Longitudes in Paris. 

Also, Ostwald : Outlines of General Chemistry; and, Muir and Wil- 
son : The Outlines of Thermal Chemistry. 



THERMAL RELATIONS THERMOCHEMISTRY. 181 

Exothermous and Endothermous Compounds. Those sub- 
stances whose formation is attended by the evolution of energy 
(heat), are called exothermoiis compounds, while those sub- 
stances whose formation is attended by an absorption of 
energy (heat), are called endothermous compounds. 

The latter as a rule, are very unstable substances, for the 
tendency of all matter is to assume that state of equilibrium, 
which, is most stable under existing conditions, and as already 
stated, in every chemical reaction, the tendency is to form 
those products whose formation gives rise to the evolution of 
the greatest quantity of heat. 

The Language of Thermochemistry. The ordinary chem- 
ical formulas and equations express relations by mass, that is 
to say, in addition to showing the substance or substances 
concerned in a reaction, and the substance or substances 
produced, they show the amounts of the different factors in- 
volved. 

Thus, the equation. 

Na + 01 = NaCl 

not only expresses the fact, that the element sodium combines 
with the element chlorine to form the compound sodium 
chloride, but it also shows, that this reaction takes place 
between 23 parts by weight of sodium and 35.5 parts by 
weight of chlorine, and that 23 + 35.5 = 58.5 parts by weight 
of sodium chloride are produced. 

If, in addition to this, it be desired to indicate the amount 
of energy involved in a chemical reaction, for instance, in the 
reaction above given, the equation must be extended, so as to 
show the amount of heat involved, for chemical energy, it 
will be remembered, is here to be measured in thermal units. 

By experiment it has been found, that the formation of 
from Na and Ci is accompanied by the evolution of 



182 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

97600 gramme-calories, and in order to indicate this fact, the 
equation above given, viz. : 

Na + 01 = NaCl 
must be written as follows : 

Na + Cl = NaCl + 97,600 g. c. 

This shows, that 23.0 grammes of Na and 35.5 grammes of 
Cl, together contain the same amount of energy as 58.5 
grammes of NaCl plus 97,600 g. c. 

This equation can be variously transformed. 

Thus for instance : 

(1) NaCl = Na + Cl - 97,600 g. c. 

which means, that in order to decompose NaCl into its con- 
stituents, 97,600 gramme-calories must be furnished. 
Or, again : 

(2) Na.-f Cl - NaCl = 97,600 g. c. 

This shows, that 97,600 gramme-calories is the difference in 
energy between Na plus Cl and NaCl. 

To furnish another illustration of thermochemical expres- 
sion: 

H + I = HI - 6100 g. c. 

This shows, that the formation of hydro-iodic acid from 
iodine (solid), and from hydrogen, is attended by an absorp- 
tion of heat, equivalent to 6100 gramme-calories. 

By transforming above equation algebraically : 

HI = H + I -f 6100 g. c. 

From this it will be seen, that a breaking up of HI into its 
constituents II and I, is accompanied by an evolution of 6100 
gramme-calories. 



THERMAL RELATIONS THERMOCHEMISTRY. 183 

Most of the data expressing the energy of chemical reac- 
tions, have been obtained at, or are referred to, a normal tem- 
perature of 18 C. The mass-amounts of the substances 
involved in these reactions always correspond to the atomic 
or the molecular masses of the substances, expressed in 
grammes. The thermal unit employed is either the gramme- 
calorie as here used, or a value 1000 times as great, and termed 
the kilogramme-calorie. 

The condition in which the substances exist, i.e. whether 
in the solid, the liquid, or the gaseous state, exercises an im- 
portant bearing on the amount of energy associated with the 
same. Very frequently the reactions studied, take place in 
large quantities of water. This, within certain limits, does 
not affect the thermal relations, and the symbol Aq (aqua) is 
used to indicate water when it thus exists as a passive factor 
in a reaction. 

Energy-equations. The examples thus far given, illustrate 
the heat of formation of an exothermous and of an endother- 
mous compound. Very often however, it is not possible to 
measure the thermo-chemical values of a given reaction 
directly, and in these instances, use is made of the funda- 
mental principle, that the initial and final stages alone, deter- 
mine the amount of heat of a chemical reaction. 

All that is required, is to execute and to measure any two 
reactions in which the initial and the final substances take 
part, and to devise a series of equations by means of which all 
intermediate reactions can be eliminated. 

As already stated, the heat of formation of a compound is 
merely the difference between the chemical energy of the 
compound formed, and that of the elements which form it. 

Na -f Cl = NaCl + 97,600 g. c., 

signifies that the heat of formation of sodium chloride is 
97,600 gramme-calories, as before stated. 

Therefore, 97,600 g. c, is the loss of energy experienced by 



184 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

the sodium and the chlorine in forming the compound sodium 
chloride. 

The absolute magnitudes of the quantities of energy in- 
volved, are unknown. If the energy of the elements be taken 
as zero, and the quantities of energy be figured therefrom, 
then, if: Na and Cl = 0, the equation: 

Na + Cl = NaCl + 97,600 g. c. 
can be written : 

-f = NaCl + 97,600 g. c. 
and this corresponds to: 

- 97,600 g. c. = NaCl. 

From this it follows, that in energy-equations, the heats of 
formation of compounds with their signs changed, can be sub- 
stituted for the formulae of these compounds, and this princi- 
ple is frequently used in thermochemical calculations. 

The following selected examples will illustrate the solving 
of thermochemical problems. 

EXAMPLE I Calculate the heat of formation of carbon monoxide. 
The data obtained by experiment, are : 

C + 2O = CO 2 + 97,OOOg. c. (A) 
CO -f O = CO 2 -f 68,000 g. c. (B) 

Subtracting B from A : 

C -f 2O - CO - O = 29,000 g. c. 
Hence : 

= CO-i-29 > OOOg. c. 



The heat of formation of CO is therefore 29,000 g. c. 
EXAMPLE II. Determine the heat of formation of hydrobromic acid, 
from the following data ; 



THERMAL RELATIONS THERMOCHEMISTRY. 185 

A. (KBr -f Aq) + iC! 2 = (KC1 + Aq) + UBr-+Aq) 11, 478 g. c. 

B. ^H 2 -f iCl a + Aq = (HC1 -f Aq) 39,315 g. c. 

C. (KOH-f "Aq) + (HCl + Aq) = (KC1 + Aq) 13,750 g. c. 
D.(KOH + Aq) + (HBr4-Aq) = (KBr + Aq) 13,750 g. c. 

E. ^Br 2 4- Aq = ($Br s -f Aq) 539 g. c. 

F. HBr -f Aq = (HBr -f Aq) 19,940 g. c. 

From A : 

1. (KC1 -|- Aq) = 11,478 -f (KBr + Aq) - (|Br a -f Aq). 

From E : 

(iBr, 4- Aq) = 539. 
Hence : 

2. (KC1 4- Aq) = 10,939 + (KBr + Aq). 

From C: 

(KC1 + Aq) = 13,750 + (KOH + Aq) + (HC1 + Aq). 



(HC1 4- Aq) = 39,315. 
Hence : 

3. (KC1 -|- Aq) = 53,065 4- (KOH + Aq). 

Placing the second members of equations No. 2 and No. 3 equal to 
each other : 

10,939 4- (KBr 4- Aq) = 53,065 + (KOH 4- Aq). 

4. (KBr 4- Aq) = 42,126 + (KOH + Aq). 

From D : 

5. (KBr 4- Aq) = 13,750 -f (KOH -f Aq) 4- (HBr + Aq). 

Placing the second members of equations No. 4 and No. 5 equal to 
each other : 

42,126 _j_ (KOH 4- Aq) = 13,750 + (KOH + Aq) 4 (HBr + Aq). 



186 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 
Hence : 

6. (HBr + Aq) = 28,376. 

In F. the heat of solution of HBr is given = 19,940. 
Hence : 

H + Br = HBr = 28,376 - 19,940, 

and the heat of formation of HBr is therefore equal to 8436 gramme 
calories. 



PHOTO-CHEMISTRY. 187 



CHAPTER XIII. 

PHOTO-CHEMISTRY. 

Introductory. Light, one form taken by the radiant energy 
emanating from the sun, is a powerful agent in effecting 
chemical changes. 

It can induce chemical union between substances, it can 
cause the decomposition of chemical compounds, and, in cer^ 
tain instances it can produce important alterations in the 
physical, as well as in the chemical, properties of the matter 
subjected to its influence. 

Chemical Union. A mixture of hydrogen and chlorine, 
if kept in the dark, will remain practically unchanged. On 
exposure to diffused light chemical combination will grad- 
ually ensue, but, if a mixture of these gases be exposed to 
direct sunlight their union is accomplished instantaneously 
and with great violence ; an explosion usually accompanying 
the reaction. 

Chemical Decomposition. Chlorine gas can be kept un- 
changed in aque'ous solution for a long time, provided it be 
carefully guarded from the light. Exposed to its influence the 
water is partially decomposed, hydrochloric acid is formed 
and oxygen liberated. 

Potassium iodide is decomposed by sunlight, iodine being 
set free. Concentrated nitric acid suffers partial decomposi- 
tion if acted on by light ; some of the oxides of nitrogen are 
formed, and these impart a yellow or brown coloration to the 
otherwise colorless acid. 

Many organic coloring matters fade and bleach, because 



188 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

light promotes the affinity of the atmospheric oxygen for two 
of their principal constituents, carbon and hydrogen. 

Most silver salts are blackened by the action of light, and 
it is on this action of light upon some of the silver salts, that 
the art of photography is based. A plate of glass, or of some 
other transparent material, is coated with iodide of silver, 
one of the silver compounds most sensitive to light. The 
plate thus prepared is placed in a camera, and the image of 
the object which is to be photographed is allowed to fall 
upon it. The plate is then immersed in a solution of ferrous 
sulphate or of some other reducing agent, and thereby the 
iodide of silver, which has been acted upon by the light, is 
more or less blackened and the picture is thus developed. 

In order to fix the picture and avoid any further action of 
the light on the plate, the iodide of silver which remains 
is removed by washing with a solution of potassium cyanide, 
or of sodium thiosulphate, commonly termed, sodium hypo- 
sulphite. The plate thus prepared constitutes the negative. 
On this of course, those parts of the image which in the object 
pictured were brightest, appear most dark, for from them 
came the greatest amount of light, and this light affected the 
iodide of silver directly in proportion to its intensity. 

To print pictures from a negative, the latter is placed on a 
surface, generally paper, coated with chloride of silver, and 
then light is allowed to fall upon it. The rays of light of 
course pass most readily through the undarkened portions of 
the negative, and thus produce in the film of chloride of 
silver a darkening, a distribution of light and shade, which 
is exactly the reverse of that existing on the negative. The 
picture thus formed the positive is then fixed, made per- 
manent, by the use of proper reagents, and the photograph is 
finished. 

But most important of all, must be counted the transfor- 
mation of radiant energy into chemical energy, through the 
agency of plants. Plants absorb carbon dioxide from the air, 



PHOTO-CHEMISTRY. 189 

and under the influence of sunlight this compound is decom- 
posed into carbon and oxygen; the former is stored in the 
plant, the latter is returned to the atmosphere. 

That green plants, in sunlight, will purify air containing 
carbon dioxide, was noticed by Priestley as early as 1772. The 
full importance of this process in the economy of Nature was 
however pointed out only by Justus von Liebig, almost seventy 
years later. 

Physical Changes. Among the most frequently cited phe- 
nomena of this description is the transformation of the com- 
mon, colorless variety of phosphorus into its red amorphous 
modification; this change of outward form and color is more- 
over accompanied by very great alterations in the chemical 
properties of the substance. 

The influence which light exercises on the crystallization 
of inverted sucrose solutions, has been made the subject of 
study by the author. Three solutions of invert-sugar were 
prepared from chemically pure sucrose; the first contained 
90.9$, the second 80.6$ and the third 58.0$ of invert-sugar. 

These solutions were placed into twenty-four glass flasks 
and these were divided into four groups A, B, C, D, of six 
flasks each. Each of these groups contained the following 
samples : 

90.9$ invert-sugar. Sol. : slightly acid 

90.9" " " " neutralized 

80.6" " " " slightly acid 

80.6" " " " neutralized 

58.0" " " " slightly acid 

58.0" " " " neutralized. 

Group A. was exposed to direct sunlight, group B. to diffused 
daylight, group C. to the rays of an electric arc-light, group D. 
was kept in darkness. 

As a full account of the interesting relations brought out 
in this investigation would here not be in place, mention 



190 LECTURE-NOTES OK THEORETICAL CHEMISTRY. 

shall only be made of the fact, that crystallization by which 
is meant transformation of the entire fluid contents of the 
flasks into the solid state, was effected in five of the flasks 
exposed to direct sunlight, before a single one of the other 
series attained to this condition. 

The series exposed to diffused dayfcght was the next to 
experience this transformation,, and this, while the solutions 
which were kept in darkness, for the greater part still retained 
their fluidity. 

Mode of Action. The chemical action of light depends 
upon its absorption this has been proved by experiment. 

As a substance does not absorb all wave-lengths of light 
alike, the chemical effects which the different color-rays 
exercise on a body are not identical. It has been determined 
that the chemical effect of light is dependent upon the color 
of the light and upon the nature of the body on which it 
acts. 

The short wave-lengths of light, the violet rays, are gener- 
ally held to be the most powerful in inducing chemical changes. 
However, in the work performed in plants the decomposition 
of carbon dioxide into its constituents, the red and the yellow 
rays are the principal agents, and in fact, all rays of light are 
capable of producing chemical effects. 

An hypothesis advanced to explain the chemical action of 
light holds, that the vibrations of the luminiferous ether 
excite in the substance acted upon, corresponding vibrations, 
that is to say, vibrations of the same period as those of the 
ether. The molecules which thus receive this supply of energy, 
are thrown into commotion, and the atoms, constituting these 
molecules, will tend to assume different positions. If this 
disturbance results in the production of more stable molecular 
systems, for instance, in the decomposition of a compound 
into its constituents, some of the radiant energy absorbed 
may be used for this purpose and remain in the system as 
bound energy. 



PHOTO-CHEMISTRY. 191 

Measurement of the Chemical Activity of Light. Attempts 
to effect such measurement, have been made in various ways. 
Senebier prepared a number of papers coated with argentic 
chloride, upon which light of a known intensity was allowed 
to act for a certain time. The amount of blackening which 
these papers experienced, depended of course upon the inten- 
sity of the light acting upon them, and upon the time of 
their exposure. In this manner, a sort of scale was obtained, 
which was of value for comparative measurements. 

Bunsen and Roscoe perfected a method, originally indicated 
by Draper, in which the formation of hydrogen chloride by 
the action of light, is made the basis of operations. Hydrogen 
and chlorine gases, in the proportion of their chemical equiv- 
alents are introduced into a thin glass bulb, the lower half of 
which is blackened, and in which water has been placed. 
This bulb is in connection with a measuring tube, which 
terminates in another vessel, also containing water. 

The light falling upon the mixture of hydrogen and chlo- 
rine, causes their chemical union, forming hydrochloric acid 
gas, and this is at once absorbed by the water. 

The consequent diminution in volume causes the water in 
the measuring tube to move towards the bulb wherein the 
hydrochloric acid was formed. The amount of water thus 
moved, is ascertained from the scale on the tube, and this 
affords a measure of the activity of the light, which has in- 
duced the chemical union of the hydrogen and the chlorine. 



192 LECTTRE-XOTES OX THEORETICAL CHEMISTRY. 



CHAPTER XIV. 
ELECTRO-CHEMISTRY. 

Introductory. The proof that chemical energy can be 
transformed into electrical energy, is easily given. 

Pun? zinc and pure platinum are not attacked by dilute 
sulphuric acid, whether these metals are immersed singly, or 
together, only provided, that they do not come into contact 
with each other. The instant however, that contact is estab- 
lished between them, either by placing them together, or by 
connecting them by some piece of metal, the zinc will be 
attacked by the sulphuric acid and will commence to dissolve, 
while bubbles of a g^s will appear on the surface of the plati- 
num. 

The connecting wire will at the same time be found to have 
become endowed with certain properties which it did not 
possess before it served to connect the pieces of metal, and 
which properties it loses, the instant that its connection with 
one or both of the metals is broken, or. when one of the latter 
is removed from the liquid. 

This clearly demonstrates the fact, that the energy set free 
by action of the sulphuric acid on the zinc, has become trans- 
formed into a form of energy which is capable of passing from 
the place of its liberation, and is capable of doing work else- 
where in its course, in the so-called electrical circuit, which 
then becomes the seat of the electrical current. 

The existence of this electric current can be shown to be 
due entirely and only to the chemical action between the acid 
and the metal: the amonnt of electricity generated, stands in 



ELECTRO-CHEMISTRY. 193 

direct relation to the amounts of chemicals, zinc and sul- 
phuric acid, involved in the process. 

Electrical energy must be regarded as the product of two 
factors, quantity and tension. This latter is also termed 
electro-motive force, or potential. The electro-motive force 
in its more general sense, is the force which tends to move the 
electricity from one point of the circuit to another; its more 
specific meaning will be defined later. 

The electro motive force, in establishing and maintaining 
an electrical current, has to overcome a certain amount of 
f rictional resistance ; the work which the electro-motive force 
does in overcoming this frictional resistance, appears as heat. 

Electrolysis. If the electric current is made to pass through 
a certain class of conductors, solutions of acids, salts, etc., cer- 
tain chemical changes take place in the system, simultaneous 
with the passing of this current, and the energy which these 
chemical changes represent, forms the remaining part of the 
work done by the electro-motive force in establishing and 
maintaining the electrical circuit. 

Chemical decomposition brought about by a current of 
electricity is termed, electrolysis. 

The substance decomposed, is called an electrolyte, and the 
constituents produced, are known as ions. The poles are 
called electrodes. The metals of salts, metallic radicals, and 
the hydrogen of acids, are always liberated at the negative 
electrode (cathode), which is that electrode in connection 
with the metal most strongly attacked by the acid ; these ions 
are termed positive ions, or cathions. The acid radicals, oxy- 
gen, chlorine, bromine, iodine, the group hydroxyl, etc., are 
set free at the positive electrode (anode), and are termed 
negative ions, or anions. 

Only certain classes of compounds are capable of serving as 
electrolytes. 

The Ion Theory. From certain phenomena it appears 
probable, that it is not the electric current which effects the 



194 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

decomposition of compounds into ions, but that these ions 
pre-exist in all solutions which can serve to conduct an 
electric current. 

This view was first suggested by Williamson (1851) and 
independently by Clausius, six years later. Clausius assumed, 
that the presence of only a very few free ions in a solution 
was necessary in order to make such a solution a conductor 
of electricity. 

The atoms of the base and the acid, constituting the salt in 
solution, were not supposed to be firmly united to one another, 
but were, in virtue of molecular encounters, supposed to 
readily enter into new combinations. Thus, molecule I, 
formed of one atom of base B and one atom of acid radical A, 
and molecule II, also formed of one atom of the same base B 
and the same acid radical A, would both be readily decom- 
posed, and give rise to the formation of two new molecules 
of the same compound. One of these newly-formed molecules 
would consist of base B, of the original molecule I in combi- 
nation with acid radical A of original molecule II, and the 
other newly-formed molecule would consist of base B of the 
original molecule II combined with the acid radical A, of 
original molecule I. 

While these exchanges were going on, the electricity was 
supposed to make use of some of these momentarily free 
atoms for its transportation to the electrodes. 

Electrolytic Dissociation. However, in 1887, this theory, 
which failed to account for many phenomena, was replaced by 
Arrhenius by a theory which is now known as, the theory of 
electrolytic dissociation. 

This investigator reached the conclusion, that in electrolytic 
solutions, for instance in aqueous solutions of strong acids and 
bases, these substances are either wholly, or at least in great 
part, dissociated, that is to say, that their constituents are 
present in the form of free ions. In dilute solutions the dis- 
sociation of a substance into free ions, is most perfect. For 



ELECTRO-CHEMISTRY. 195 

the laws governing this dissociation are the same as those 
which control gaseous dissociation, and the dissociation of 
gases increases with a decrease of pressure. But in solution, 
we have the osmotic pressure analogous to gaseous pressure, 
and the osmotic pressure of a solution is decreased as the 
concentration of the solution is lessened, therefore, dilution 
decreases the osmotic pressure and correspondingly encourages 
dissociation into ions. 

Attention must be called to the fact, that an ion of an 
element does not correspond to a free atom of that element. 

For instance, if a solution of sodium chloride were used as an 
electrolyte, the ions would of course consist of sodium and of 
chlorine. But the sodium ions and the chlorine ions, as long 
as they exist as ions, that is to say, as long as they are charged 
with electricity, do not behave like the ordinary free atoms 
of sodium and of chlorine. The sodium ion, for instance, will 
not decompose water, while, as is well known, sodium not 
electrically charged will do this most energetically; likewise, 
the ion chlorine behaves diiferently from an ordinary free 
atom of chlorine. But when the charges of electricity which 
the ions bear, have been discharged at the respective electrodes, 
the elements resume their customary properties and functions. 
Ions may be either atoms of elements, or groups of atoms. 

The anions carry negative, the cathions bear positive elec- 
tricity. These ions of course move towards opposite elec- 
trodes; those charged with positive electricity move towards 
the negative electrode, and those charged with negative elec- 
tricity travel to the positive electrode, and there discharge 
their electricity. Thus, in decomposing a solution of sulphate 
of copper, the copper atoms, after giving up their charge of 
electricity, are precipitated as metallic copper, while the S0 4 
radical decomposes the water in which the reaction takes 
place, forming sulphuric acid and liberating oxygen gas. 

An interesting point to be mentioned in this connection is 
the fact, that chemical reactions for certain substances can be 



196 LECTURE -NOTES ON THEORETICAL CHEMISTRY. 

* 

obtained only, when the substances tested for, can appear, on 
electrolysis, as free ions, and not, when these substances occur 
as constituents of complex ions. 

Thus, for instance, chlorine is generally tested for by 
nitrate of silver. But while this test is a very satisfactory 
one for free chlorine, for chlorine when existing in the form 
of hydrochloric acid and in the form of numerous metallic 
chlorides, it will not answer for the detection of chlorine 
when in the form of potassium chlorate. Careful examina- 
tion shows, that this test for chlorine can be obtained only in 
such of its compounds, which, when subjected to electrolysis, 
yield the chlorine as a free ion. 

The tendency of the ions of an electrolyzed solution to 
recombine chemically, gives rise to an electro-motive force, 
which is called the electro-motive force of polarization, and 
which has been regarded as offering a means to measure the 
chemical affinity of the ions. 

Electrical Units. Whenever an electric current is estab- 
lished in a closed circuit, and performs work at different 
points of its path, any and all chemical changes which are 
induced, will be found to be the exact chemical equivalents 
of each other. These quantitative relations were first enun- 
ciated by Faraday, and are expressed in his laws. Before 
however passing on to a consideration of these relations, the 
system of units employed for the measurement of electrical 
energy requires mention. 

In the centimetre-gramme-second system, generally referred 
to as the C. G. S. system of units, the centimetre is adopted as 
the unit of length, the gramme as the unit of mass, and the 
second as the unit of time. 

From these fundamental units there are derived the 
C. G. S., or as they are sometimes called, the " absolute" units 
of velocity, acceleration, force, work, energy, and, heat ; they 
are as follows : 



ELECTRO-CHEMISTRY. 197 

UNIT OF VELOCITY: the velocity of oiie centimetre per 

second. 
UNIT OF ACCELERATION: an acceleration of one centi- 

met^e-per-second per second. 
UXIT OF FORCE: that force which acting for one second 

on a mass of one gramme, imparts to it a velocity of 

one centimetre per second. It is named the Dyne. 
UXIT OF WORK: the work done in moving a body one 

centimetre against the force of one Dyne. It is named 

the Erg. 
UXIT OF EXERGY : the Erg as above defined, for the energy 

of a system is measured by the work it can accomplish. 
UXIT OF HEAT: the amount of heat required to raise the 

temperature of one gramme-mass of water from to 

1 C. It is termed the gramme-calorie. 

Two systems of electrical units are derived from these fun- 
damental units : the electro-static, and the electro-magnetic 
units. The practical units employed in the measurement of 
electrical quantities follow; they are derived from the electro- 
magnetic units. 

The Ohm = unit of resistance. 

(10 9 C. G. S. units of resistance.) 
It is the resistance offered by a column of mercury 
106.28 c.m. long and 1 sq. mm. in section at C. 
The Volt = unit of electromotive force. 

(10 8 C. G. S. units of electro-motive force.) 
The electro-motive force of a Daniell cell is 1.079 volts. 
The Coulomb = unit of quantity. 

(10- 1 C. G. S. units of quantity.) 

It is the quantity of electricity which in one second flows 
through the section of a conductor between the ends of 
which there is an electro- motive force of 1 Volt, and 
the resistance of which is 1 Ohm. 



198 LECTURE-NOTES ON THEOEETICAL CHEMISTRY. 

The Ampere = unit of current-strength. 

(1CT 1 C. G. S. units of current.) 

It is the current produced by 1 Volt through 1 Ohm, 
i. e., 1 Coulomb per second, is 1 Ampere. 
The Watt = unit of power, i.e., the rate of doing work. 

(10 7 C. G. S. units of power.) 

It is the power conveyed by a current of 1 Ampere 
in 1 second through a difference of potential of 1 Volt. 
The Farad = unit of capacity. 

(10- 9 C. G. S. units of capacity.) 
It is the capacity of a condenser that will be raised 
to a potential of one Volt by a charge of one Coulomb. 
(As a condenser of this capacity is too large to be con- 
structed, the Micro-farad = 0.000001 Farad is adopted 
as the working unit of electrical capacity. ) 
The Joule = unit of work or heat. 

(10 7 C. G. S. units of work. ) 

It is the mechanical equivalent of the heat generated 

per second by a current of 1 Ampere flowing through a 

resistance of 1 Ohm, i. e. the heat generated by 1 Watt. 

To indicate quantities a million times as great as those here 

given, the word mega- is prefixed to the term; in order to 

denote quantities a million times as small, the prefix micro- is 

employed; while quantities one thousand times as small are 

designated by the prefix milli-. 

The system of index notation, as used above in expressing 
values in the C. G. S. system, has been adopted for the sake 
of convenience and in order to economize space. Only the 
significant figures of a quantity are written down, the ciphers 
are indicated by an index written above. 
Thus: 

100 = 10 X 10 = 10 3 
1000 = 10 X 10 X 10 = 10 3 
10000 = 10 X 10 X 10 X 10 = 10* 
and thus 90,000 can be written : as 9 X 10 4 



ELECTRO-CHEMISTRY. 199 

Decimals have negative indices. Thus 0.000128 is ex- 
pressed by: 128 X 10~ f as it is equal to 128 X .000001. 

Quantitative Relations. The following formulae express 
some of the relations existing between electrical units. 

Let,, 

C denote Ampere, 

E " Volt, 

R " Ohm, 

W " Watt, 

H " Heat-work, 

Q " Quantity of electricity, 

t " time, 
Then, 

C = ^ (Ohm's Law.) 
E= Cx R 



W= CxE 

F* 
W- 

~ R 

TT= C*R 

H^ C'Rt (Joule's Law.) 
ff= QE 
Q=Ct 

The amount of the ion set free in a given time, at an 
electrode, is dependent upon the strength of the current, and 
is directly proportional to it. This is one of Faraday's elec- 
trolytic laws. 

One Coulomb of electricity, in passing through water, 
liberates an amount of hydrogen which has been variously 
stated to be * : 

* S. P. Thompson : Elementary Lessons in Electricity and Magnet- 
ism. 1892. 



200 LECTURE-NOTES ON THEORETICAL CHEMISTRY. 

0.000010352 gramme, Lord Rayleigh 
0.000010354 " Kohlrausch 
0.000010415 " Mascart 

This quantity is termed the electro-chemical equivalent of 
hydrogen. 

The electro-chemical equivalent of any element is obtained 
by dividing the atomic mass of the element by its valence, 
and then multiplying the resulting quotient by 0.000010352. 

Thus, the electro - chemical equivalents, (expressed in 
gramme per Coulomb), of a few of the elements are as follows : 

Silver ................ -^- 8 X .000010352 = 0.0011180 

c compounds } Tf X 00010352 = - 0003293 



fn'cuprous compounds } ^ X -000010352 = 0.0006584 

/"* ** Q 

Zinc ................. ~|^- X .000010352 = 0.0003379 

Oxygen .............. ^ X .000010352 = 0.0000828 

The actual weight in grammes of any ion liberated by 
electrolysis is obtained by the formula : 

w = zct, 

where, w = weight in grammes, 

z the electro-chemical equivalent of the ion, 

c = strength of current in Amperes, 

t = time in seconds during which the current flows. 

This principle has been practically applied by Edison in 
measuring the quantities of electricity supplied to stations 
from central electric plants. A solution of cupric sulphate 
is electrolyzed between two copper electrodes. The anode 
will be dissolved by the current, while the equivalent amount 



ELECTRO-CHEMISTRY. 201 

of copper will be deposited on the cathode. Therefore, if 
one of these electrodes is weighed before and after the pas- 
sage of the electric current, the quantity of electricity which 
has passed can be readily calculated. 

If a metal which has been deposited by an electric current 
is made to undergo combustion, or is dissolved in acid, its 
potential energy will be given up in the form of heat, and the 
equivalent amount of work can be easily calculated, provided, 
that the mechanical equivalent of heat has been ascertained. 

As stated by Thompson : " The electro-motive force of any 
chemical reaction is equal to the product of the electro-chem- 
ical equivalent of the separated ion into its heat of combi- 
nation, expressed in dynamical units." Embodying this in a 
formula, and exemplifying by a problem * : 

e = zHJ 
where, z absolute electro-chemical equivalent, in grammes, 

of the ion. f 

H number of heat-units evolved by 1.0 gramme of 
the substance on entering into the combination 
considered. 

J = Joule's equivalent. 

Example : Find the electro-motive force of hydrogen tend- 
ing to unite with oxygen. 

For hydrogen, z = 0.00010352, 

H = 34,000 gramme-calories, 
J = 42 X 10 6 

.00010352 X 34,000 X 42 X 10 6 = 1.47 X 10 s absolute units 
of electro-motive force. As 10 8 absolute units of electro- 
motive force are equivalent to one Volt, the value found 
corresponds to 1.47 Volts. 

* S. P. Thompson, loc. cit. p. 389. 

f The absolute electro-chemical equivalents are ten times as great as 
the values previously given for the electro-chemical equivalents, for the. 
Coulomb is 0.1 of the C, G. S. unit of quantity. 



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The date of the latest edition, known to the writer, deter- 
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Asterisks indicate the books consulted. 



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1892. * WINDISCH, K. Die Bestimmung des Moleculargewichts in 

theoretischer und praktischer Beziehung. Berlin. 

1893. ' ADRIANCE, J. S. Laboratory Calculations and Specific 

Gravity Tables. 2d Edition. New York. 

1893. BERTHELOT, M. Traite pratique de calorime*trie chimique. 
Paris. 

1893. DUHEM, P. Introduction a la mecanique chimique. Gand. 

1893. HANTZSCH, A. Grundriss der Stereochemie. Breslau. 

1893. MEYER, L. Grundziige der Theoretischen Chemie. 2d Edi- 
tion. Leipzig. 

1893. NERNST, W. Theoretische Chemie vom Standpunkte der 
Avogadro'schen Regel und der Thermodynamik. Stuttgart. 

1893. VAN LAAR, J. J. Die Thermodynamik in der Chemie. 
Leipzig. 



INDEX OF SUBJECTS. 



PAGE 

Absolute unit of force 156 

Absolute unit of work 157 

Absorption, coefficient of 144 

Adhesion 158 

Affinity, chemical 158 

Affinity, coefficient of 164 

Affinity, tables of 162 

Agents, oxidizing 91 

Aids in determining atomic mass 59 

Aims of chemical philosophy 3 

Aims of chemistry 3 

Alchemists, notation of 29 

Alchemy, age of 2 

Algebraic method of writing chemical equations 97 

Alloys 149 

American system of spelling and pronunciation of chemical terms. 45 

Analogues, atomic 139 

Analysis of gases 128 

Analysis, proximate 128 

Analytical method of writing chemical equations 93 

Anious 193 

Anode 193 

Areometers 13 

Atom, definition 5 

Atomic analogues. . . 139 

Atomic heat 61 

Atomic mass 53 

Atomic mass, aids in determining 59 

Atomic mass, determination of 57 

Atomic mass, standards of 54 

Atomic masses, table of 55 

Atomic volumes, diagram of 141 

215 



216 ItfDE^X OF SUBJECTS. 

PAGE 

Avogadro, law of , 119 

Baume areometers 14 

Bauine degrees, true values of 15 

Bergman's system .- 32 

Berzelius on chemical symbols and nomenclature 40 

Bibliography 202 

Black's list of synonyms 33 

Boiling-point, elevation of v 75 

Boyle, law of , 18 

Calorific intensity 174 

Calorific power 173 

Calhions 193 

Cathode 193 

Charles, law of 18 

Chemical activity of light, measurement of 191 

Chemical affinity 158 

Chemical affinity, measurement of 161 

Chemical affinity, nature of 159 

Chemical calculations 89 

Chemical decomposition, induced by light 187 

Chemical equations 89, 90 

Chemical equivalent 58 

Chemical formulae 69, 89 

Chemical philosophy, aims of 3 

Chemical problems, calculation of 99 

Chemical terms, oldest 29 

Chemical union, induced by light 187 

Chemism 159 

Chemistry, aims of 3 

Chemistry, origin and meaning of the term 2 

Coefficient of absorption 144 

Coefficient of affinity 164 

Cohesion 1 58 

Colloids 153 

Combustion 173 

Conductivity, equivalent 165 

Conductivity, molecular. . , 165 

Conservation of energy 157 

Constituents of compounds, calculation of 100 

Constitutional formulae 89 

Crith, value of . 115 



INDEX OF SUBJECTS. 217 

PAGE 

Crystalloids 153 

Curves, graphic . v 139 

Dalton's symbols 39 

Deductive sciences, definition 1 

Depression of the freezing-point method 75 

Determination of atomic mass 57 

Determination of valence 66 

Difference Method 108 

Diffusion 150, 152 

Dilute solutions 149 

Dissociation, electrolytic.. 194 

Dumas' Method 20 

Dyne, the 156 

Effusion method 19 

Equations, energy , 183 

Equivalent, chemical 58 

Equivalent conductivity 165 

Equivalent, electro-chemical 200 

Electrical energy 193 

Electrical units 196, 197, 198 

Electrical units: quantitative relations 199 

Electro-chemical equivalent * 200 

Electro-chemistry 192 

Electrodes 193 

Electrolysis 193 

Electrolyte 193 

Electrolytic dissociation 194 

Elevation of boiling-point method 75 

Eudothermous compounds 181 

Energy.. 5, 155 

Energy, bound 162 

Energy, conservation of 157 

Energy, electrical 193 

Energy-equations 183 

Energy, free 162 

Energ3 r , kinetic 157 

Energy, measurement of 157 

Empirical f ormulse 69, 89 

Equations, chemical 89, 90, 93 

Erg, the 157 

Exothermous compounds 181 



218 INDEX OF SUBJECTS. 

PAGE 

Explosions, method of 130 

Force 155 

Force, absolute unit of 156 

Force, definition 5 

Force, gravity unit of 156 

Force, measurement of 155 

Formulae, chemical 69, 89 

Formulae, constitutional 89 

Formulae, empirical 69, 89 

Formula from percentage composition 101 

Formulae, mineralogical 101 

Formulae, molecular 71, 89 

Formula, weight and volume 127 

Freezing-point, depression of 75 

French system of nomenclature 34 

Gases, analysis of 128 

Gases, determination of specific gravity ' . 20 

Gases in gases, solution of 143 

Gases in liquids, solution of 144 

Gases in solids, solution of 145 

Gases, table of 116 

Gases, volume relations of 115 

Geoffrey's symbols 31 

Germanic system of nomenclature 39 

Gramme-calorie 168 

Graphic curves 139 

Gravitation 158 

Gravity unit of force 156 

Gravity unit of work 157 

Hassenfratz and Adet's symbols 37 

Heat, latent 1 69 

Heat, mechanical equivalent of 168 

Heat, specific 1 69 

Heat units 168 

Henry's law 145 

Hofmann's, von, method 24 

Hydrogen, occluded 145 

Hypothesis, definition 4 

latro-chemistry, age of 2 

Ice calorimeter method 170 

Index notation, system of . . . , , , 198 



INDEX OF SUBJECTS. 219 

PAGE 

Indirect analysis, methods of 107 

Inductive sciences, definition 1 

Interchange, chemical, laws of 92 

Invert-sugar solutions, action of light on, 189 

Ion theory, the 193 

Isomerism 84 

Isomorphism 63 

Kilogramme-calorie 168 

Kinetic energy 157 

Knowledge, definition 1 

Laplace 161 

Latent heat 169 

Law of Avogadro 119 

Law of Boyle or Muriotte 18 

Law of Charles 18 

Laws of chemical combination 52 

Laws of chemical interchange 92 

Law of definite proportions 52 

Law of Henry 145 

Law of multiple proportions 52 

Law, periodic, the 133, 134 

Law of volumes 119 

Light, action on invert-sugar solutions 189 

Light, chemical decomposition induced by 187 

Light, chemical union induced by 187 

Light, mode of action , 190 

Light, physical changes induced by 189 

Liquids in gases, solution of 145 

Liquids in liquids, solution of 145 

Liquids in solids, solution of 147 

Lowering of vapor- pressure method 74 

Magnetic rotation of polarized light 84 

Manner of designating valence 65 

Mariotte, law of 18 

Mass, definition 5 

Mass and volume in gases, relation between 124 

Matter, definition 5 

Maximum valence 68 

Measurement of chemical affinity 161 

Measurement of chemical activity of light 191 

Measurement of energy , 157 



220 I&DEX OF SUBJECTS. 

PAGE 

Measurement of force 155 

Mecbauical equivalent of heat 168 

Meudeleeffs predictions 139 

Mendeleeff's table of atomic masses 136 

Method of explosions 130 

Methods of indirect analysis 107 

Meyer, Lothar, table of atomic masses 138 

Meyer's, V., method 26 

Mineralogical formulae.. 101 

Minimum valence 68 

Mixtures, method of 171 

Molecular conductivity 165 

Molecular formulae 71, 89 

Molecular mass, calculation of 99 

Molecular mass, determination of 72 

Molecular refraction 81 

Molecular refraction-equivalent - 83 

Molecular volume 79 

Molecule, definition 5 

Molecules, structure of 78 

Motion, definition 5 

Negative bond method of writing chemical equations 96 

Newlands' table of atomic masses 135 

Nomenclature in the seventeenth century 31 

Nomenclature, French system of 34 

Notation of the alchemists. . . 29 

Occluded hydrogen 145 

Osmose 150 

Osmotic pressure 73, 150 

Osmotic pressure, measurement of 151 

Oxidizing agents 91 

Percentage composition from formula 101 

Periodic law, the 133, 134 

Periodicity of properties of elements 142 

Photo-chemistry 187 

Photography 188 

Physical changes induced by light , . . 189 

Polarized light, magnetic rotation of 84 

Predictions, Mendeleeff's 139 

Present system of symbols and nomenclature 41 

Pressure, osmotic. ... 73, 150 



IXDEX OF SUBJECTS. 221 

PAGE 

Properties of elements, etc. , periodicity of 142 

Proximate analysis 128 

Reducing agents 92 

Refraction-equivalent, molecular 83 

Refraction, molecular 81 

Refractive power, specific 83 

Relation between mass and volume in gases 124 

Relations between specific gravity, degrees Bauine and Brix 15 

Relations between specific gravity, mass and volume 8 

Residue method 107 

Rest, definition. > 5 

Science, definition 1 

Solids in gases, solution of 147 

Solids in liquids, solution of 147 

Solids in solids, solution of 149 

Solutions 143 

Solutions, dilute 149 

Solution of gases in gases ; 143 

Solution of gases in liquids 144 

Solution of gases in solids 145 

Solution of liquids in gases 145 

Solution of liquids in liquids 145 

Solution of liquids in solids 147 

Solution of solids in gases 147 

Solution of solids in liquids 147 

Solution of solids in solids 149 

Specific gravity, definition 7 

Specific gravity of gases and vapors 17 

Specific gravity of gases, determination of 19 

Specific gravity of liquids 11 

Specific gravity of solids 9 

Specific gravity of vapors 20 

Specific gravity, standards of 7 

Specific heat 62, 169 

Specific heat, determination of 169 

Specific refractive power 82 

Standards of atomic mass 54 

Standards of specific gravity 7 

Standard of valence 64 

Stereo- chemistry 85, 86 

Stoichiometry 5 



222 INDEX OF SUBJECTS. 

PAGE 

Structure of molecules 78 

Substitution method 108 

Symbols of Hassenf ratz and Adet 37 

Tables of affinity 162 

Tables of atomic masses 55 

Mendeleeff's 136 

Meyer, Lothar 138 

Newlands' 135 

Table of gases, Wiechmann's 116 

Temperature 167 

Theory, definition 4 

Thermal relations 167 

Thermo-chemistry, language of 178, 181 

Thermo-chemistry, laws of 179 

Time method 172 

Units, electrical 196 

Valence 63 

Valence, determination of *. 66 

Valence, manner of designating 65 

Valence, maximum 68 

Valence, minimum 68 

Valence, standard of 64 

Valence, variable 65 

Vapor-density, determination of 72 

Vapors, specific gravity, determination of 20 

Vapor-pressure, lowering of 74 

Volumes, atomic, diagram of . . , 141 

Volume, definition 5 

Volumes, law of 119 

Volume, molecular 79 

Volume relations of gases 115 

Von Hofmann's system of nomenclature 44 

Weight and volume formula 127 

Weight, definition ,. 5 

Wiechmann's table of gases ,.r 116 

Work, absolute unit of .-. 157 

Work, definition 5 

Work, gravity unit of 157 



INDEX OF NAMES CITED. 



PAGE 

Adet 37 

Arago 86 

An henius 194 

Avogadro 6 

Baume 32 

Bedson 137 

Bergman 160, 163 

Bernoulli 164 

Bertbelot 179 

Berthollet 35, 160, 163 

Berzelius 6, 54, 160 

Biot 86,88 

Black 33,39 

Bolton 46 

Bottomley 97 

Briihl 83 

Bunseu 144,164, 191 

Chandler, C. F 14 

Clarke 54 

Clausius 119, 164, 194 

Cooke 133 

Dalton 6, 52, 53, 54, 144, 145 

Davy 39,160 

Debus 164 

Dobereiner 133 

Draper 191 

Dumas 133 

Edison 200 

Faraday 84, 165, 196 

Fick 153 

Fourcroy 35 

Galileo 159 

Gay-Lussac 6, 119,148, 161 

223 



224 INDEX OF NAMES CITED. 

PAGE 

Geber 29 

Geoffroy 162 

Gernez , 88 

Gladstone 134, 164 

Gmeliii 183 

Graham 153 

Greenaway 136 

Guldberg 163, 164 

Hart 46 

Hasseu fratz 37 

Helmholtz, vcm 162, 165 

Hofmaiiu, vou 44 

Homberg 6 

Howe 46 

Humboldt, von 6, 119 

Johnson 96 

Joule 160, 164 

Kainensky 136 

Kirwau 163 

Kohlrausch . 165, 200 

Kopp 79 

Kremer 133 

Landolt , 83 

Lavoisier 6, 35, 52, 161 

Le Bel 86, 88 

Liebig, von 189 

Lorentz 82 

Lorenz 82 

Lorenz, von 16 

Macquer 32 

Mascart 200 

Maxwell 164 

Mayer 160 

Mendeleeff 134, 136, 139 

Meyer, L 135, 137 

Mitscherlich 63 

MOller 148 

Morveau, de 34, 161 

Muir 147, 164, 180 

Newlands , 134 

Newton.. . 160 



INDEX OF NAMES CITED. 225 

PAGE 

Norton 46 

Olding 133 

Ostwald 54, 144, 147, 164, 165 

Perkins 84 

Pettenkofer 133 

Pfaundler 164 

Pfeffer 151 

Priestley 189 

Proust 6, 52 

Quesneville 41 

Rayleigh, Lord 200 

Regnault 145 

Remseu 66 

Reusch 86 

Richter, J. B 6 

Rose, H 164 

Roscoe 191 

Schwanert 97 

Seuebier 191 

Sorby 148 

Button 131 

Thompson, S. P 198, 201 

Thoinseu, J 180 

Thomson, Sir W 165 

Thomson 6, 39 

Van Helmont 6 

Van'tHoff 86, 87, 88, 150, 151, 164 

Von Helmholtz 162, 165 

Von Hof mann 44 

Von Humboldt 6, 119 

Von Liebig 189 

Von Lorenz 16 

Waage 163, 164 

Weber 153 

Wenzel 6, 161 

Wiechmann 14, 17, 116, 189 

Williams , 137 

Williamson 164, 194 

Wilson 180 

Wislicenus 85 

Wurtz.. 66 



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